Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
CONIC SECTIONS
XI C
α β
THE INTERSECTION OF A PLANE WITH A CONE,
THE SECTION SO OBTAINED IS CALLED A
CONIC SECTION
V
m
Lower
nappe
Upper
nappe...
TYPES OF CONIC SECTIONS
CIRCLE
A CIRCLE IS THE
SET OF ALL
POINTS ON A
PLANE THAT ARE
EQUIDISTANT
FROM A FIXED
POINT ON A
PLANE.
O
P(x,y)
(h,k)
C
P(x,y)
O (0,0)
x² + y² = r² (x – h) ² + (y – k) ² = r²
α β
When β = 90°, the section is a circle
Standard Equation...
TYPES OF CONIC SECTIONS
ELLIPSE
AN ELLIPSE IS THE SET
OF ALL THE POINTS ON A
PLANE,
WHOSE SUM OF
DISTANCES FROM TWO
FIXED TWO REMAINS
CONSTANT.
P
...
α β
O
(0,c)
(0,-c)
(-b,0) (b,0)
(0,-a)
(0,a)
x² y²
a² b²
— —+ = 1—+
x² y²
b² a²
— = 1
(-c ,0) (c, 0)
When α < β < 90°, the...
.
TYPES OF CONIC SECTIONS
A PARABOLA IS THE
SET OF ALL POINTS
IN A PLANE THAT
ARE EQUIDISTANT
FROM A FIXED POINT
A
B
V
PARABOLA
(VERTEX)
F
( focus)
...
α
β
F(a,0)O
x=-a
y² = 4ax
X' X
Y'
Y
F(-a,0) O
x=+a
y² = -4ax
X' X
Y'
Y
F(0,-a)
O
y = a
x² = 4ay
X' X
Y'
Y
F(0,a)
O
y = -a
...
TYPES OF CONIC SECTIONS
HYPERBOLA
F ( focus)V
(verte
x)
A
B
A HYPERBOLA IS THE
SET OF ALL POINTS,THE
DIFFERENCE OF WHOSE
DISTANCES FROM TWO
FIXED ...
α β
Transverse
axis
F
Conjugate axis
F(c ,0)(a ,0)( -c ,0)
(-a ,0)
O
F
F(0 ,c)
(0 ,a)
(0 ,-c)
(0 ,-a)
O
¹
¹
²
²
x² y²
a² b...
HYPERBOLIC PARABOLOIDSUNDIAL
THERMAL POWER PLANT
Conic Section Standard Eq. General Eq.
Circle x² + y² = r² (x – h) ² + (y – k) ² = r²
Parabola y² = 4ax (y-k)² = 4a(x+h)
E...
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Upcoming SlideShare
Loading in …5
×

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

8,862 views

Published on

Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.

Published in: Education

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

  1. 1. CONIC SECTIONS XI C
  2. 2. α β THE INTERSECTION OF A PLANE WITH A CONE, THE SECTION SO OBTAINED IS CALLED A CONIC SECTION V m Lower nappe Upper nappe Axis Generator l This is a conic section.
  3. 3. TYPES OF CONIC SECTIONS
  4. 4. CIRCLE A CIRCLE IS THE SET OF ALL POINTS ON A PLANE THAT ARE EQUIDISTANT FROM A FIXED POINT ON A PLANE. O P(x,y)
  5. 5. (h,k) C P(x,y) O (0,0) x² + y² = r² (x – h) ² + (y – k) ² = r² α β When β = 90°, the section is a circle Standard Equation General Equation
  6. 6. TYPES OF CONIC SECTIONS
  7. 7. ELLIPSE AN ELLIPSE IS THE SET OF ALL THE POINTS ON A PLANE, WHOSE SUM OF DISTANCES FROM TWO FIXED TWO REMAINS CONSTANT. P P P F F ¹ ³² ²¹
  8. 8. α β O (0,c) (0,-c) (-b,0) (b,0) (0,-a) (0,a) x² y² a² b² — —+ = 1—+ x² y² b² a² — = 1 (-c ,0) (c, 0) When α < β < 90°, the section is an ellipse Vertical Ellipse Horizontal Ellipse (0,-b) (0,b) (a,0)(-a,0)
  9. 9. .
  10. 10. TYPES OF CONIC SECTIONS
  11. 11. A PARABOLA IS THE SET OF ALL POINTS IN A PLANE THAT ARE EQUIDISTANT FROM A FIXED POINT A B V PARABOLA (VERTEX) F ( focus) 1 2 3 4O P 1 P2
  12. 12. α β F(a,0)O x=-a y² = 4ax X' X Y' Y F(-a,0) O x=+a y² = -4ax X' X Y' Y F(0,-a) O y = a x² = 4ay X' X Y' Y F(0,a) O y = -a x² = -4ay X' X Y' Y When α = β, the section is an parabola Horizontal Parabola Horizontal Parabola Vertical Parabola Vertical Parabola
  13. 13. TYPES OF CONIC SECTIONS
  14. 14. HYPERBOLA F ( focus)V (verte x) A B A HYPERBOLA IS THE SET OF ALL POINTS,THE DIFFERENCE OF WHOSE DISTANCES FROM TWO FIXED POINTS IS CONSTANT V (verte x) F ( focus)
  15. 15. α β Transverse axis F Conjugate axis F(c ,0)(a ,0)( -c ,0) (-a ,0) O F F(0 ,c) (0 ,a) (0 ,-c) (0 ,-a) O ¹ ¹ ² ² x² y² a² b² — —- = 1 - y² x² a² b² — —- = 1 When 0 ≤ β < α; the plane cuts through both the nappes & the curves of intersection is a hyperbola
  16. 16. HYPERBOLIC PARABOLOIDSUNDIAL THERMAL POWER PLANT
  17. 17. Conic Section Standard Eq. General Eq. Circle x² + y² = r² (x – h) ² + (y – k) ² = r² Parabola y² = 4ax (y-k)² = 4a(x+h) Ellipse Hyperbola x² y² a² b² — —+ = 1 (x-h)² (y-k)² a² b² — + — = 1 x² y² a² b² — —- = 1 (x-h)² (y-k)² a² b² — - — = 1

×