The document describes the definition and properties of a parabola. It states that a parabola is the locus of a point such that its distance from a fixed point (the focus) is equal to its distance from a fixed line (the directrix). The document derives the standard equation of a parabola, x^2 = 4ay, and defines the key elements of a parabola including the vertex, focus, directrix, and focal length. It provides an example of calculating these elements for a given parabola equation.

1. The Parabola As a Locus
y
x

2. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
line (directrix)
x

3. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  line (directrix)
x

4. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  line (directrix)
x
y  a

5. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  line (directrix)
x
y  a

6. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a

7. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a)

8. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a) d PS  d PM

9. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a) d PS  d PM
 x  0   y  a    x  x    y  a 
2 2 2 2

10. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a) d PS  d PM
 x  0   y  a    x  x    y  a 
2 2 2 2
x2   y  a    y  a 
2 2

11. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a) d PS  d PM
 x  0   y  a    x  x    y  a 
2 2 2 2
x2   y  a    y  a 
2 2
x 2  y 2  2ay  a 2  y 2  2ay  a 2

12. The Parabola As a Locus
y A point moves so that its distance
from a fixed point (focus) is
equal to its distance from a fixed
S  0, a  P  x, y  line (directrix)
x
y  a M ( x, a) d PS  d PM
 x  0   y  a    x  x    y  a 
2 2 2 2
x2   y  a    y  a 
2 2
x 2  y 2  2ay  a 2  y 2  2ay  a 2
x 2  4ay

13. x 2  4ay

14. x 2  4ay
vertex:  0,0 

15. x 2  4ay
vertex:  0,0 
focus:  0, a 

16. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a

17. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units

18. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y

19. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32

20. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32
a 8

21. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32
a 8
focal length = 8 units

22. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32
a 8
focal length = 8 units

23. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32
a 8 (0,0)
focal length = 8 units

24. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y
4a  32
8
a 8 (0,0)
focal length = 8 units

25. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 (0,0)
focal length = 8 units

26. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 (0,0) 8
focal length = 8 units

27. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units

28. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
b) y  4 x 2

29. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
4

30. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a 
4

31. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a 
4
1
a
16

32. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a 
4
1
a focal length =
1
unit
16 16

33. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a 
4
1
a focal length =
1
unit
16 16

34. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a 
4
1 (0,0)
a focal length =
1
unit
16 16

35. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
1
b) y  4 x 2  x 2  y
1 4
4a  1
4 16
1 (0,0)
a focal length =
1
unit
16 16

36. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
 1
1 focus is  0, 
b) y  4 x  x  y
2 2
 16 
1 4
4a  1
4 16
1 (0,0)
a focal length =
1
unit
16 16

37. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
 1
1 focus is  0, 
b) y  4 x  x  y
2 2
 16 
1 4
4a  1
4 16
1 (0,0)
a
1
1 16
16 focal length = unit
16

38. x 2  4ay
vertex:  0,0 
focus:  0, a 
directrix: y  a
focal length: a units
e.g. (i) Find the focus, focal length and directrix;
a) x 2  32 y focus is (0,8)
4a  32
8
a 8 directrix is y  8 (0,0) 8
focal length = 8 units
 1
1 focus is  0, 
b) y  4 x  x  y
2 2
 16 
1 4
4a  1
4 directrix is y   1
1 16 16
a 1 (0,0) 1
16
16 focal length = unit
16

39. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2

40. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2
a  2

41. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2
a  2 x 2  4  2  y

42. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2
a  2 x 2  4  2  y
x 2  8 y

43. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y
x 2  8 y

44. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3
x 2  8 y

45. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y

46. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x

47. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin

48. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin
 x  p   4a  y  q 
2

49. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin
 x  p   4a  y  q 
2
vertex:  p, q 

50. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin
 x  p   4a  y  q 
2
vertex:  p, q 
focus:  p, q  a 

51. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin
 x  p   4a  y  q 
2
vertex:  p, q 
focus:  p, q  a 
directrix: y  q  a

52. (ii) Find the equation of the parabola with;
a) focus  0, 2  , directrix y  2 b) focus  3,0  , directrix x  3
a  2 x 2  4  2  y a3 y 2  4  3 x
x 2  8 y y 2  12 x
Vertex NOT at the origin
 x  p   4a  y  q 
2
vertex:  p, q 
focus:  p, q  a 
directrix: y  q  a
focal length: a units

53. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units

54. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1
2

55. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1
2
 x  3  8  y  1
2
x2  6 x  9  8 y  8

56. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1
2
 x  3  8  y  1
2
x2  6 x  9  8 y  8
8 y  x 2  6 x  17
y   x  6 x  17 
1 2
8

57. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1
2
x2  6 x  9  8 y  8
8 y  x 2  6 x  17
y   x  6 x  17 
1 2
8

58. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17
y   x  6 x  17 
1 2
8

59. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8

60. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3
2

61. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3
2
 y  1  8  x  3
2
y 2  2 y  1  8 x  24

62. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3
2
 y  1  8  x  3
2
y 2  2 y  1  8 x  24
8 x  y 2  2 y  25
x   y  2 y  25 
1 2
8

63. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3  y  1  4  2  x  3
2 2
 y  1  8  x  3
2
y 2  2 y  1  8 x  24
8 x  y 2  2 y  25
x   y  2 y  25 
1 2
8

64. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3  y  1  4  2  x  3
2 2
 y  1  8  x  3  y  1  8  x  3
2 2
y 2  2 y  1  8 x  24 y 2  2 y  1  8 x  24
8 x  y 2  2 y  25
x   y  2 y  25 
1 2
8

65. e.g. (i) Find the equation of the parabola with vertex  3,1 and
focal length 2 units
 x  3  4  2  y  1  x  3  4  2  y  1
2 2
 x  3  8  y  1  x  3  8  y  1
2 2
x2  6 x  9  8 y  8 x 2  6 x  9  8 y  8
8 y  x 2  6 x  17 8 y   x2  6x 1
y   x  6 x  17  y    x  6 x  1
1 2 1 2
8 8
 y  1  4  2  x  3  y  1  4  2  x  3
2 2
 y  1  8  x  3  y  1  8  x  3
2 2
y 2  2 y  1  8 x  24 y 2  2 y  1  8 x  24
8 x  y 2  2 y  25 8 x   y 2  2 y  23
x   y  2 y  25  x    y  2 y  23
1 2 1 2
8 8

66. (ii) focus (2,8) and directrix y = 10

67. (ii) focus (2,8) and directrix y = 10

68. (ii) focus (2,8) and directrix y = 10
a y  10

69. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8

70. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a 1

71. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a  1 vertex is (2,9)

72. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a  1 vertex is (2,9)  x  2   4 1 y  9 
2

73. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a  1 vertex is (2,9)  x  2   4 1 y  9 
2
 x  2   4  y  9 
2

74. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a  1 vertex is (2,9)  x  2   4 1 y  9 
2
 x  2   4  y  9 
2
x 2  4 x  16  4 y  36

75. (ii) focus (2,8) and directrix y = 10
a y  10
a
 2,8
2a  2
a  1 vertex is (2,9)  x  2   4 1 y  9 
2
 x  2   4  y  9 
2
x 2  4 x  16  4 y  36
4 y   x 2  4 x  20
y    x  4 x  20 
1 2
4

76. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3

77. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3

78. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x

79. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2

80. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2

81. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2

82. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a

83. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12

84. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3

85. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3
 focal length = 3 units

86. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3,
 focal length = 3 units

87. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
 focal length = 3 units

88. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
 focal length = 3 units
vertex =  3, 1

89. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
 focal length = 3 units
vertex =  3, 1

90. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
(3, 1)
 focal length = 3 units
vertex =  3, 1

91. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
3
(3, 1)
 focal length = 3 units
vertex =  3, 1

92. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
3
(3, 1)
 focal length = 3 units
vertex =  3, 1
focus =  3, 2 

93. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
3
(3, 1)
 focal length = 3 units 3
vertex =  3, 1
focus =  3, 2 

94. (iii) Find the vertex, focus, focal length, directrix of 12 y  x 2  6 x  3
12 y  x 2  6 x  3
12 y  3  x 2  6 x
12 y  3  9   x  3
2
12 y  12   x  3
2
12  y  1   x  3
2
4a  12
a3 vertex: (3, –1)
3
(3, 1)
 focal length = 3 units 3
vertex =  3, 1
focus =  3, 2 
directrix: y  4

95. Exercise 9B; 1,2 try at home
4 (use definition)
6ace etc, 7ac, 8ace, 9ace, 10ac, 11bd, 12a
Exercise 9C; 3 to 8 ace etc, 10ac, 11ace, 12