Precalculus Honors
Circles, Ellipses, and Hyperbolas Review 1
Name___________________________
Date____________________________
1. Find the equation of the circle with center (-6, 2) and radius r =
2 3
.
5
2. Find the equation of the circle with diameter endpoints (1, 5) and (-1, 7).
3. Find the equation of a circle with center (-3, 5) and with circumference of 8π units.
4. Find the equation of the circle with center (-2,4) and which contains the point (3,2)
Precalculus Honors
Circles, Ellipses, and Hyperbolas Review 1
Name___________________________
Date____________________________
5. Find the equation of the circle with center (2,-1) and tangent to the line y = 1.
6. Find the equation of the ellipse with vertices (3, 0), (-3, 0), (0, 5) and (0, -5).
7. Find the equation of the ellipse with vertices (5, 1), (3, 1), (4, 6), and (4, -4).
8. Find the equation of the ellipse with vertices (-2, -4) and (-2, 6) and foci (-2, 4) and
(-2, -2).
Precalculus Honors
Circles, Ellipses, and Hyperbolas Review 1
Name___________________________
Date____________________________
9. Find an equation of the ellipse with foci at (1,4) and (3,4) and major axis 4 units long.
10. Find an equation of the ellipse with vertices (0, -1) and (12, -1) and minor axis of length
6.
11. Determine the type of conic listed below. Determine the general form for this particular
conic, indicate the coordinates of the center (or vertex), indicate the x- and/or y- radii,
and if necessary, the equations of the slant asymptotes. 25 y 2 − 9 x 2 − 50 y − 54 x − 281 = 0
12. Determine the equation of the conic which satisfies the following conditions:
a. The coordinates of the foci are f1 (-2, -3) and f 2 (-2, 5)
b. The distance from f1 to a point X on the curve and the distance from f 2 to the
same point X add to 12.
Precalculus Honors
Circles, Ellipses, and Hyperbolas Review 1
Name___________________________
Date____________________________
13. Determine the equation of the ellipse whose vertices (major axis) are the same ordered
− x2 y2
pairs as the foci of :
+
= 1 . (Hint: vertices of hyperbola = foci of ellipse)
64 36
14. The foci of a hyperbola are at (2, 7) and (2, -7) and the distance between the vertices is
8 3 . Determine the equation of the hyperbola and the equations of the asymptotes.
15. The orbit of the earth around the sun is elliptical in shape with the sun at one focus and
major axis length of 185.5 million miles. If the distance between the foci is 3.16 million
miles, determine: (a) an equation for the orbit (b) how close the earth gets to the sun and
(c) the greatest possible distance between the earth and the sun.