The document discusses different conic sections including circles, parabolas, and their standard forms. A circle is defined as all points equidistant from a fixed center point. The standard form of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. A parabola is defined as all points equidistant from a fixed focus point and directrix line. The standard forms of parabolas that open up, down, left or right are presented based on the location of the vertex, focus and directrix.
8. x2
y 2
r 2
The Standard Form of a circle with a center at
(0,0) and a radius ‘r’ is....
e x a m p l e : -
x2
y 2
16
Center(0,0)
Radius(4units) 8
9. (x-h)2
(y - k ) 2
r 2
The Standard Form of a circle with a center at
(h,k) and a radius ‘r’ is....
e x a m p l e : -
( x - 3 ) 2
(y - 3 ) 2
2
Center(3,3)
Radius(2units)
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11. What is a parabola ?
A parabola is the set of all points in a plane
such that each point in the set is equidistant
from a line called the directrix and a fixed
point called the focus.
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13. Parabola in real life…
Four parabolas are created given the four "legs"
of the Eiffiel Tower
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14. The Standard Form of a Parabola that opens to
the right and has a vertex at (0,0) is……
y2
4px
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15. The Parabola that opens to the right and has a vertex
at (0,0) has the following characteristics……
a. p is the distance from the vertex of the parabola
to the focus or directrix
b. This makes the coordinates of the focus (p,0)
c. This makes the equation of the directrix x = -p
d. The makes the axis of symmetry the x-axis (y = 0)
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16. The Standard Form of a Parabola that opens to
the left and has a vertex at (0,0) is……
y2
-4px
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17. The Parabola that opens to the left and has a vertex at
(0,0) has the following characteristics……
a. p is the distance from the vertex of the parabola to
the focus or directrix
b. This makes the coordinates of the focus(-p,0)
c. This makes the equation of the directrix x = p
d. The makes the axis of symmetry the x-axis (y = 0)
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18. The Standard Form of a Parabola that opens to
the up and has a vertex at (0,0) is……
x2
4py
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19. The Parabola that opens to up and has a vertex at
(0,0) has the following characteristics……
a) p is the distance from the vertex of the parabola to
the focus or directrix
b) This makes the coordinates of the focus (0,p)
c) This makes the equation of the directrix y = -p
d) This makes the axis of symmetry the y-axis(x = 0)
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20. The Standard Form of a Parabola that opens to
the down and has a vertex at (0,0) is……
x2
-4py
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21. The Parabola that opens to down and has a vertex at
(0,0) has the following characteristics……
a. p is the distance from the vertex of the parabola
to the focus or directrix
b. This makes the coordinates of the focus (0,-p)
c. This makes the equation of the directrix y = p
d. This makes the axis of symmetry the y-axis(x = 0)
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