SOLUTION: Find a set of parametric equations for the conic section or line below;
Ellipse: Center: (5,-3); Vertices: 6 units above and below the center; Endpoint of minor Axis: 2 units left
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Question 1143991: Find a set of parametric equations for the conic section or line below;
Ellipse: Center: (5,-3); Vertices: 6 units above and below the center; Endpoint of minor Axis: 2 units left and right of center.
A. x=5+6cos t, y=-3+2 sin t
B. x=5-2cos t, y=-3-6 sin t
C. x=5+2cos t, y=-3+6 sin t
D. x=2+5cos t, y=6-3 sin t
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Let's start with a generic set of parametric equations and see how it relates to the equation of an ellipse in rectangular coordinates.
The parameter is t; eliminate it using sin^2+cos^2=1.
The center is (a,c); the semi-major and semi-minor axes are (in some order) b and d.
Now use that analysis for the given ellipse.
The center is (a,c) = (5,-3), so the constants in the parametric equations for x and y must be 5 and -3, respectively. That eliminates answer choice D.
The semi-major axis is 6, in the y direction, so d is 6. That makes answer choice C the only possible correct answer.
It can be seen that answer choice C is in fact correct, because it shows the semi-minor axis having length b=2.
ANSWER: C. x=5+2cos t, y=-3+6 sin t
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