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Alg Bas Rev

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Conic Sections See video! Circle Ellipse Parabola Hyperbola Where do parabolas occur? Occurrences/uses of an ellipse? Where do parabolas occur? – PowerPoint PPT presentation

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Title: Alg Bas Rev


1
Conic Sections
See video!
Circle Ellipse
Parabola Hyperbola
2
Circle
Standard Equation of a Circle
P(x, y)
(with radius of r and center at (h,k)
2
2
2
(
x

h
)
(

y

k
)

r


r
gt 0
C(h, k)
With center at (0,0), this simplifies to
x2 y2 r2
3
Completing the Square
To complete the square of the quadratic
expression     add the square of one-half the
coefficient of x that is, add
The resulting expression can be factored as a
perfect square
4
Reflective properties of parabola and ellipse
  1. Focus of Parabola
  2. Reflective Properties of Ellipses

5
Where do parabolas occur?
6
Standard Equations of a Parabola with Vertex at
(0, 0)
1. y ax2 Vertex (0, 0) Symmetric
with respect to the y-axis.
Vertex (h, k)
a gt 0 (opens up) a lt 0 (opens down)
2. x ay2 Vertex (0, 0)
Symmetric with respect to the x-axis.
Vertex (h, k)
a lt 0 (opens left) a gt 0 (opens right)
7
Occurrences/uses of an ellipse?
8
Standard Equations of an Ellipse with Center at
(0, 0)
9
Standard Equations for Translated ConicsII
Ellipses
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