1. Find the parametric equations for each of these circles:
|
a
|
x2 + y2 = 16 |
b
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x2 + y2 = 1 |
|
c
|
(x + 3)2 + (y + 4)2 = 9 |
d
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(x − 1)2 + (y − 2)2 = 100 |
|
e
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x2 + (y − 5)2 = 25 |
f
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(x − 6)2 + y2 = 81 |
2. Give the parametric equations for each parabola:
|
a
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y2 = 12x |
b
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y2 = 40x |
|
c
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(y − 5)2 = 8x |
d
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(y + 2)2 = 12x |
|
e
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(y − 1)2 = 4(x − 1) |
f
|
(y + 1)2 = 8(x − 2) |
3. Give the parametric equations for these ellipses and hyperbolas:
|
a
|
 |
b
|
 |
|
c
|
 |
d
|
 |
4. Given each set of parametric equations, eliminate the parameter and form an equation in x and y only:
|
a
|
x = 5cos t , y = 4 sin t |
b
|
x = 6cos θ , y = 2sin θ |
|
c
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x = cos t − 5, y = sin t − 3 |
d
|
x = 2cos w -1, y = 7sin w + 3 |
|
e
|
x = 0.25cos t, y = 0.2sin t |
f
|
x = 2.5cos v, y = 0.5sin v |
5. a. Find 
for each of the following pairs of parametric equations:
|
a
|
x = 3cos t − 3, y = 3sin t − 4 |
b
|
x = 2t2 , y = 4t + 5 |
|
c
|
x = 4cos t , y = 5sin t |
d
|
x = 5sec t − 3 , y = 4tan t + 1 |
6. By eliminating t, find the Cartesian equation of the curve x = t − 3, y = 4t2
7. x = t + 3 and y = 2t + 5. Find the cartesian equation of this function and sketch its graph.
8. A curve is given parametrically by x = 5secθ and y = 3tan θ
a. Find the Cartesian equation of this curve.
b. Sketch the curve, marking clearly any intercepts and the point P where θ = 4π / 3
c. Find
9. A curve y = p(x) has parametric equations x = -1 / 2t and y = 4t
a. Eliminate t to find the Cartesian equation of the curve.
b. Find the gradient of the curve at the point when t = 3
c. For what values of t is this curve discontinuous?
10. Write down the parametric equations of the conic 
