Precalculus Honors
Chapter 6 Test Review
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Date_____________________________
1. Write an equation of the circle with center (-2, 5) that is tangent to the line
5 x − 4 y = 11 .
2. An ellipse has vertex (-10,0), focus(-8, 0) and center at the origin. Find an equation of
the ellipse.
Sketch the graph. Find the important features.
3. x 2 + y 2 − 4 x + 8 y + 11 = 0
4. y 2 − 6 y + 16 x + 25 = 0
5. x 2 − 4 y 2 − 2 x + 16 y − 19 = 0
6. 9 x 2 + 16 y 2 − 18 x − 64 y − 71 = 0
Precalculus Honors
Chapter 6 Test Review
7. Find the vertex, focus, and directrix of each parabola.
a) 6 x − x 2 = 8 y + 1
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b) x = − y 2 − 3
8. Find an equation of the circle that contains the points (6,2 ), (− 2,−4 ), (− 1,3) .
Solve the following systems.
x2 + y2 = 8
9. 2
x −y=6
10.
( x + 3) 2 + y 2 = 1
x = −y2
11. Find the equation of the parabola with focus (8, 10) and vertex (8, 6).
12. Find an equation of the ellipse with foci at (1, 4) and (3, 4) and major axis 4 units
long.
Precalculus Honors
Chapter 6 Test Review
Name____________________________
Date_____________________________
13. Find the center, vertices, foci, and asymptotes of the hyperbola.
64 x 2 − 25 y 2 − 256 x − 150 y − 1569 = 0
14. Find the vertex, focus, directrix, and axis of symmetry, then graph the parabola.
y 2 + 10 y + 133 = 12 x
15. Find the center, vertices, and foci of 81x 2 + 64 y 2 − 972 x + 512 y − 1244 = 0 .
Precalculus Honors
Chapter 6 Test Review
Name____________________________
Date_____________________________
16. According to Kepler’s Laws, planets have elliptical orbits, with the sun at one of the
foci. The farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets
to the sun is 4.4 billion kilometers. Find the equation of the orbit of Pluto.
17. Find the key information for the graph 16 x 2 + 16 y 2 − 24 x + 8 y − 22 = 0
18. The ellipse represented by 4 x 2 + 3 y 2 = 84 and 3x 2 + 4 y 2 = 91 intersect in 4 points,
all of which lie on a circle.
a) Determine the coordinates of the four points of intersection.
b) Determine the equation of the circle that contains those points.