1. Find the focus of the parabola
Find the focus of the parabola. y 2 = 4 x Choose the correct answer from the following.
(1, 0)
(- 2, 0)
(0, 4)
(0, - 2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Find an equation for the parabola, that has a focal diameter 36 and the focus on the negative y-axes. Choose the correct answer from the following.
x 2 = - 36y
x 2 = 36y
x 2 = - 9y
y 2 = 9x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. (-10, 0) and (10, 0) (-6, 0) and (6, 0) (-8, 0) and (8, 0)
Find the vertices of the ellipse. {image} . Choose the correct answer from the following:
(-10, 0) and (10, 0)
(-6, 0) and (6, 0)
(-8, 0) and (8, 0)
None of these choices 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. The ancillary circle of an ellipse is the circle with radius equal to half the length of the minor axis and a center the same as the ellipse. The ancillary circle is thus the largest circle that can fit within an ellipse. Find an equation for the ancillary circle of the ellipse x y 2 = 16. Choose the correct answer from the following.
x 2 + y 2 = 4
x 2 + y 2 = 16
x 2 + y 2 = 1
x 2 + y 2 = 9
None of these choices 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Find the equation for the hyperbola with foci {image} and vertices {image} . Choose the answer from the following:
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

6. y 2 = 5.6(x + 4) y 2 = 16(x + 1.4) 2 x 2 = 5.6(y - 4) y = 5.6(x + 4) 2
Find an equation for the conic whose graph is shown. {applet} Choose the answer from the following:
y 2 = 5.6(x + 4)
y 2 = 16(x + 1.4) 2
x 2 = 5.6(y - 4)
y = 5.6(x + 4) 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

7. Determine the equation of the conic {image} in XY-coordinates when the coordinate axes are rotated through the angle {image} Choose the answer from the following :
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

8. Use a rotation of axes to eliminate the xy-term in the equation {image} Choose the answer from the following :
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

9. Write a polar equation of an ellipse that has eccentricity 0
Write a polar equation of an ellipse that has eccentricity 0.7 and vertex at the point {image} Choose the answer from the following :
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50