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Which polar equation represents an ellipse?

r= 1/3+2cos theta
r= 3/2+3 sin theta
r= 5/2+2 sin theta
r= 2/2-3 sin theta

User Brkr
by
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1 Answer

6 votes

Answer:


r=(1)/(3+2cos\theta)

Explanation:

Let us write the equations in standard form:


r=(1)/(3+2cos\theta) \implies r=((1)/(3) )/(1+(2)/(3)\cos \theta )

We have


e=(2)/(3)\:<\:1 and


ep=(1)/(3)

Since the eccentricity of this conic is less than 1, the conic represents an ellipse.

The second equation is
r=(3)/(2+3\sin \theta).

This is a hyperbola, because eccentricity is more than 1.

The third equation is
r=(5)/(2+2\sin \theta).

This is a parabola, because eccentricity is 1.

The fourth equation is
r=(2)/(2-3\sin \theta).

This is also a hyperbola, because eccentricity is more than 1.

User Opengrid
by
7.7k points
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