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.

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4. Conic Sections
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6. What is a circle?
A circle is a locus of all the points
equidistant from a fixed point to
the outer boundary.
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7. Circles in Real Life
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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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12. Parabola in real life…
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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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