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1. |
The equation of a circle is 3x2 + 3y2 – 6x + 12y – 24 = 0. Find its center and radius. |
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A. |
(1, –2); 13 |
B. |
(–1, 2);  |
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C. |
(–1, 2); 13 |
D. |
(1, –2); |
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Hint |
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2. |
For the equation  , find the coordinates of the center of the ellipse. |
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A. |
(9, 3) |
B. |
(3, 9) |
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C. |
(-3, 2) |
D. |
(2, -3) |
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Hint |
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3. |
Find the standard form of the equation x2 - 5y2 - 2x - 10y - 9 = 0. |
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A. |
 |
B. |
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C. |
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D. |
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Hint |
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4. |
The eccentricity of a parabola is _____. |
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A. |
greater than 1 |
B. |
0 |
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C. |
sometimes 1 |
D. |
always 1 |
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Hint |
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5. |
Find the rectangular equation of the curve whose parametric equations are
x = 4 cos t and y = 4 sin t, where  . |
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A. |
x2 - y2 = 16 |
B. |
x2 + y2 = 4 |
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C. |
x2 - y2 = 4 |
D. |
x2 + y2 = 16 |
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Hint |
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6. |
Find parametric equations for the equation y = x2 + 5. |
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A. |
x = t, y = t2 + 5,  |
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B. |
x = t2 + 5, y = t, |
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C. |
x = t, y = t2 + 5,  |
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D. |
x = t, y = t2 + 5, -2 < t < 2 |
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Hint |
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7. |
Find the angle  of rotation for the graph of the equation
x2 - xy - y2 - 2x - 2y + 6 = 0. Round to the nearest degree. |
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A. |
-13° |
B. |
30° |
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C. |
52° |
D. |
-27° |
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Hint |
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8. |
Solve the system of equations x + 2 = 0 and y2 = 36 - x2 algebraically. Round to the nearest tenth. |
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A. |
(±2, 5.7) |
B. |
(-2, 5.7) |
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C. |
(-2, ±5.7) |
D. |
(-2, -5.7) |
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Hint |
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9. |
Solve the system of equations algebraically.
x2 - y2 = 12
x2 + 2y2 = 24 |
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A. |
(±4, 2), (±4, -2) |
B. |
(2, 4), (-2, -4) |
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C. |
no solution |
D. |
(4, 2), (-4, -2) |
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Hint |
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10. |
Find the distance between points (2, 4) and (-4, -1). |
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A. |
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B. |
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C. |
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D. |
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Hint |
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11. |
Find the distance between points (5, 4) and (-2, -3). Round to the nearest tenth. |
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A. |
7.1 |
B. |
3.2 |
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C. |
9.9 |
D. |
14 |
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Hint |
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12. |
Write the equation of a circle that passes through points (1, 2), (-1, 4) and (-3, 2) in standard form. |
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A. |
(x + 1) 2 + (y - 3) 2 = 4 |
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B. |
(x - 1) 2 + (y - 2) 2 = 4 |
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C. |
(x - 1) 2 + (y + 3) 2 = 4 |
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D. |
(x + 1)2 + (y - 2) 2 = 4 |
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Hint |
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13. |
Write an equation of an ellipse centered at the origin, with a = 4, b = 3 and the major axis on the y-axis. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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14. |
Find the coordinates of the center of the hyperbola with an equation of  |
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A. |
(6, -2) |
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B. |
(2 -6) |
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C. |
(-6, 2) |
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D. |
(-2, 6) |
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Hint |
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15. |
Write the equation y2 - 4y - 2x - 1 = 0 in standard form. |
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A. |
(y + 2) 2 = 2x - 5 |
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B. |
(y - 2) 2 = 2(x - 2.5) |
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C. |
(y + 2) 2 = 2(x + 2.5) |
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D. |
(y - 2) 2 = 2x + 5 |
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Hint |
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16. |
Write an equation in general form of  for T(2,-3). |
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A. |
 |
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B. |
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C. |
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D. |
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Hint |
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