April 20, 2017
sec. 9.1: Parabolas, Circles
Introduction to Conic Sections
ellipse and circle
April 20, 2017
Circles
(x - h)² + (y - k)² = r²
center: (h, k)
radius: r
Ex. Find the center and the radius:
(x + 6)² + y² = 81
April 20, 2017
Ex. Find the center and the radius:
x² + y² + 6x - 8y - 11 = 0
Parabolas
the set of all points
EQUIDISTANT from a
given point (called the
focus) and a given line
(called the directrix)
April 20, 2017
Standard Equations
4p(y - k) = (x - h)2
4p(x - h) = (y - k)2
vertex = (h, k)
p = the distance from vertex to focus
= the distance from vertex to directrix
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Ex. Find the equation of the parabola with
focus (3, 2) and vertex (-1, 2)
Find the standard form of the equation of the parabola with vertex at the
origin and focus (0, 4).
April 20, 2017
Ex. Write in standard form and find the vertex.
x² + 4x + 6y - 2 = 0
April 20, 2017