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CHAPTER 9<br />
Topics in Analytic Geometry<br />
Section 9.1<br />
Circles and Parabolas<br />
■ A parabola is the set of all points x, y that are equidistant from a fixed line (directrix) and a fixed point<br />
(focus) not on the line.<br />
■ The standard equation of a parabola with vertex h, k and<br />
(a) Vertical axis x h and directrix y k p is<br />
(x h) 2 4p( y k), p 0.<br />
(b) Horizontal axis y k and directrix x h p is<br />
(y k) 2 4p(x h), p 0.<br />
■ The tangent line to a parabola at a point P makes equal angles with<br />
(a) the line through P and the focus.<br />
(b) the axis of the parabola.<br />
Vocabulary Check<br />
1. conic section 2. locus 3. circle, center<br />
4. parabola, directrix, focus 5. vertex 6. axis<br />
7. tangent<br />
1.<br />
x 2 y 2 18 2 2.<br />
x 2 y 2 18<br />
x 2 y 2 42 2<br />
x 2 y 2 32<br />
3.<br />
5.<br />
7.<br />
Radius 3 1 2 7 0 2 4. Radius 6 2 2 3 4 2<br />
4 49 53<br />
64 49 113<br />
x h 2 y k 2 r 2<br />
x h 2 y k 2 r 2<br />
x 3 2 y 7 2 53<br />
x 6 2 y 3 2 113<br />
Diameter 27 ⇒ radius 7 6. Diameter 43 ⇒ radius 23<br />
x h 2 y k 2 r 2<br />
x h 2 y k 2 r 2<br />
x 3 2 y 1 2 7<br />
x 5 2 y 6 2 12<br />
x 2 y 2 49 8. x 2 y 2 1 9. x 2 2 y 7 2 16<br />
Center: 0, 0<br />
Center: 0, 0<br />
Center: 2, 7<br />
Radius: 7<br />
Radius: 1<br />
Radius: 4<br />
© Houghton Mifflin Company. All rights reserved.<br />
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