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1. |
Find the coordinates of the midpoint of the segment that has endpoints at (-4, 7) and (2, -11). |
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A. |
(-1, -2) |
B. |
(-2, -4) |
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C. |
(-2, -1) |
D. |
(-4, -2) |
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Hint |
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2. |
Write the general form of the equation of the circle that passes through the points at (4, 2), (–3, 1), and (–2, –6). |
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A. |
x2 + y2 + 2x – 4y – 20 = 0 |
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B. |
x2 + y2 – 2x + 4y – 20 = 0 |
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C. |
x2 + y2 + 2x + 4y – 20 = 0 |
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D. |
x2 + y2 – 2x – 4y + 20 = 0 |
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Hint |
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3. |
For the equation  , find the coordinates of the foci of the ellipse. |
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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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4. |
Find the equation of the hyperbola with foci at (8, 2) and (-4, 2) whose transverse axis is 10 units long. |
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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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5. |
Find the standard form of the equation x2 - 5y2 - 2x - 10y - 9 = 0. |
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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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6. |
Find the vertex of the parabola with equation y2 = 4x + 20. |
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A. |
(0, 5) |
B. |
(-5, 0) |
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C. |
(0, -5) |
D. |
(5, 0) |
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Hint |
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7. |
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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8. |
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 = t, y = t2 + 5, -2 < t < 2 |
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C. |
x = t2 + 5, y = t, |
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D. |
x = t, y = t2 + 5,  |
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Hint |
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9. |
Identify the graph of the equation x2 -3xy + 2y2 + 10y + 1 = 0. |
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A. |
parabola |
B. |
hyperbola |
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C. |
circle |
D. |
ellipse |
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Hint |
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10. |
Identify the graph of the equation 3x2 + 10xy + 14y2 - 6 = 0. |
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A. |
circle |
B. |
parabola |
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C. |
hyperbola |
D. |
ellipse |
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Hint |
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11. |
Solve the system of equations algebraically.
x - y + 2 = 0
x2 + y2 = 10 |
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A. |
(4, 6) |
B. |
(-1, -3), (3, 1) |
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C. |
(1, 3) |
D. |
(-3, -1), (1, 3) |
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Hint |
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12. |
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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13. |
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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14. |
Write the equation x2 + 4y2 + 8x - 8y + 16 = 0 in standard form. |
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A. |
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B. |
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D. |
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Hint |
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15. |
Write the equation of a parabola in standard form if the general form of the equation is 6x2 + 12x - y + 8 = 0 |
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A. |
(x - 1) 2 =  (y + 2) |
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B. |
(x - 1) 2 = 6(y - 2) |
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C. |
(x + 1) 2 = (y - 2) |
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D. |
(x + 1) 2 = 6(y - 2) |
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Hint |
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16. |
Solve the system of equations y+ 3 = 0 and
x2 = y2 - 9 algebraically. |
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A. |
(-3, 0) |
B. |
(3, 0) |
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C. |
(0, -3) |
D. |
(0, 3) |
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Hint |
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