Precalculus
Review
Chapter 9 - Conic Sections
“Circles, Parabolas, Ellipses, Hyperbolas”
Name_____________________________________
Date__________________Period______________
Learning Target: Students will be able to identify an equation as a circle, parabola, ellipse, or hyperbola.
Identify the following as a circle, parabola, ellipse, or hyperbola.
1. 9( x  2)2  16( y  2)2  144
A. circle
B. parabola
C. ellipse
D. hyperbola
2. y  x 2  4 x
A. circle
B. parabola
C. ellipse
D. hyperbola
3. ( x  4)2  ( y  4)2  36
A. circle
B. parabola
C. ellipse
D. hyperbola
4. 4( x  2)2  9( y  3)2  36
A. circle
B. parabola
C. ellipse
D. hyperbola
Learning Target: Students will be able to write the equation of a circle.
5. Find the equation of the circle.
(3,3)
(7,3)
(5, 0)
Learning Target: Students will be able to graph and analyze a circle.
6. What is the equation of the circle graphed below?
7. Given the circle x2  y 2  10 x  4 y  25  0, identify the center and radius.
Learning Target: Students will be able to graph and analyze vertical and horizontal parabolas.
Graph the parabolas. Identify the vertex, axis of symmetry, domain, and range of each.
8.
y  5x 2  20 x  9
9.
x  3y2  6 y  2
Vertex: ____________________________
Vertex: ____________________________
Domain: ___________________________
Domain: ___________________________
Range: ____________________________
Range: __________________ __________
Axis of symmetry: ___________________
Axis of symmetry: ___________________
Learning Target: Students will be able to graph and analyze an ellipse.
Directions: Sketch the graph of each of the following ellipses. Label your points.
10.
( x  2)2 ( y  1) 2

1
25
9
11.
25x2  4 y 2  100
Center: _____________ Vertices:_____________
Center: _____________ Vertices:_____________
Endpts: _____________ Domain:_____________
Endpts: _____________ Domain:_____________
Range:______________
Range:______________
Learning Target: Students will be able to graph and analyze a hyperbola.
Directions: Sketch the graph of each of the following hyperbolas. Label your points.
12.
( y  3)2 ( x  2)2

1
9
16
13.
x 2 ( y  2) 2

1
16
9
Center: _____________ Vertices:_____________
Center: _____________ Vertices:_____________
Domain: ____________ Range:______________
Domain: ____________ Range:______________
Learning Target: Students will be able to write equations of conic sections.
14. Write the equation for the ellipse whose center is at (0, 0), one vertex is at (0, 4), and the length of the
minor axis is 6.
15. Write the equation for the vertical hyperbola whose center is at (2, -4) and a = 3, b = 4.