2. Conic Sections - Definition
• A conic section is a
curve formed by
intersecting cone with
a plane.
• There are four types
of Conic sections.
1.Circle,2.ellipse,
3.parabola,4.hyperbola.
5. What’s in 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.
(x, y)
6. Parabola
• The Standard Form of a Parabola that opens to the right
and has a vertex at (0,0) is……
)0(42
>= aaxy
7. Parabola
• The Standard Form of a Parabola that opens to the left
and has a vertex at (0,0) is……
)0(42
>−= aaxy
8. Parabola
• The Standard Form of a Parabola that opens up and
has a vertex at (0,0) is……
ayx 42
=
9. Parabola
• The Standard Form of a Parabola that opens down and
has a vertex at (0,0) is……
ayx 42
−=
10. Parabola
• The Standard Form of a Parabola
that opens to the left and has a
vertex at (h,k) is……
)(4)( 2
hxaky −−=−
11. Parabola
• The Standard Form of a Parabola that opens up and has
a vertex at (h,k) is……
)(4)( 2
kyahx −=−
12. Parabola
• The Standard Form of a Parabola that opens
down and has a vertex at (h,k) is……
)(4)( 2
kyahx −−=−
14. What is in an Ellipse?
• The set of all points in the plane, the sum of whose
distances from two fixed points, called the foci, is a
constant. (“Foci” is the plural of “focus”, and is
pronounced FOH-sigh.)
15. Ellipse
• The standard form of the ellipse with a center at (0,0)
and a horizontal axis is……
12
2
2
2
=+
b
y
a
x
16. Ellipse
• The ellipse with a center at (0,0) and a horizontal axis
has the following characteristics……
• Vertices ( a,0)
• Co-Vertices (0, b)
• Foci ( c,0)
±
±
±
1
916
22
=+
yx
17. Ellipse
• The standard form of the ellipse with a center at (0,0)
and a vertical axis is……
12
2
2
2
=+
a
y
b
x
18. Ellipse
• The ellipse with a center at (0,0) and a vertical axis has
the following characteristics……
• Vertices (0, a)
• Co-Vertices ( b,0)
• Foci (0, c)
±
±
±
1
819
22
=+
yx
19. Ellipse
• The standard form of the ellipse with a center at (h,k)
and a horizontal axis is……
1
)()(
2
2
2
2
=
−
+
−
b
ky
a
hx
20. Ellipse
• The ellipse with a center at (h,k) and a horizontal axis
has the following characteristics……
• Vertices (h a , k)
• Co-Vertices (h, k b)
• Foci (h c , k)
±
±
±
21. Ellipse
• The standard form of the ellipse with a center at
(h,k) and a vertical axis is……
1
)()(
2
2
2
2
=
−
+
−
a
ky
b
hx
22. Ellipse
• The ellipse with a center at (h,k) and a vertical axis
has the following characteristics……
• Vertices (h, k a)
• Co-Vertices (h b , k)
• Foci (h, k c)
±
±
±
23. Hyperbola
The huge chimney of a nuclear power plant has the shape of a hyperboloid, as does
the architecture of the James S. McDonnell Planetarium of the St. Louis Science Center.
24. What is a Hyperbola?
• The set of all points in the plane, the
difference of whose distances from two fixed
points, called the foci, remains constant.
25. Hyperbola
• The standard form of the Hyperbola with a center at
(0,0) and a horizontal axis is……
12
2
2
2
=−
b
y
a
x
26. Hyperbola
• The Hyperbola with a center at (0,0) and a horizontal
axis has the following characteristics……
• Vertices ( a,0)
• Foci ( c,0)
• Asymptotes:
x
a
b
y ±=
±
±
27. Hyperbola
• The standard form of the Hyperbola with a center at
(0,0) and a vertical axis is……
12
2
2
2
=−
b
x
a
y
28. Hyperbola
• The Hyperbola with a center at (0,0) and a vertical
axis has the following characteristics……
• Vertices (0, a)
• Foci ( 0, c)
• Asymptotes: x
b
a
y ±=
±
±
29. Hyperbola
• The standard form of the Hyperbola with a center at
(h,k) and a horizontal axis is……
1
)()(
2
2
2
2
=
−
−
−
b
ky
a
hx
30. Hyperbola
• The Hyperbola with a center at (h,k) and a horizontal
axis has the following characteristics……
• Vertices (h a, k)
• Foci (h c, k )
• Asymptotes:
)( hx
a
b
ky −±=
±
±
31. Hyperbola
• The standard form of the Hyperbola with a center at
(h,k) and a vertical axis is……
1
)()(
2
2
2
2
=
−
−
−
b
hx
a
ky
32. Hyperbola
• The Hyperbola with a center at (h,k) and a vertical
axis has the following characteristics……
• Vertices (h, k a)
• Foci (h, k c)
• Asymptotes: )( hx
b
a
ky −±=
±
±