Name _____________________________ Period __________ Date ______________
Conics – Circles and Parabolas
Take Home Quiz
Show your work. Simplify fractions and radicals.
Identify the center and radius of the circle.
1. x 2   y  3  36
2
Center ________________
Radius _______________
2.
 x  4    y  5
2
2
 48
Center ________________
Radius _______________
Write the equation of the circle in standard form and then identify the center and
radius.
3. x 2  y 2  2 x  6 y  9  0
Equation _____________________
Center ________________
Radius _______________
4. 9 x 2  9 y 2  54 x  36 y  17  0
Equation _____________________
Center ________________
Radius _______________
Find the vertex, focus, and the directrix of the parabola.
5. x 2  8 y  0
Vertex ________________
Focus ________________
Directrix _____________
6.
 y  2
2
 2  x  5 
Vertex ________________
Focus ________________
Directrix _____________
7. x 2  y 2  14 y  25  0
Vertex ________________
Focus ________________
Directrix _____________
8. y  13 x 2  12 x  15
Vertex ________________
Focus ________________
Directrix _____________
Write an equation of each parabola described below.
9. Vertex (8,6); Focus (2,6)
Equation _____________________
10. Vertex (-3,-2); Focus (-3,3)
Equation _____________________
11. Focus (-4,-2); directrix: x = -8
Equation _____________________
12. Vertex (-7,4); axis of symmetry x = -7;
measure of latus rectum: 6; concave down.
Equation _____________________
13. An automobile headlight contains a parabolic reflector. A special bulb with
two filaments is used to produce the high and low beams. The filament
placed at the focus produces the high beam and the filament placed off the
focus produces the low beam.
The equation of the cross section of the reflector is y  112 x 2 . How far from
the vertex should the filament for the high beam be placed?
____________