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Find an equation equivalent to x2 - y2 = 4 in polar coordinates.

User Mohan Ram
by
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2 Answers

5 votes

Answer:

The answer is D r^2 cos2(theta) = 4

Explanation:

The person above me simplified it too much.

User Dickoa
by
8.3k points
4 votes

Answer:


r^2=4\sec 2\theta}

Explanation:

The given equation is:


x^2-y^2=4

We substitute
x=r\cos (\theta) and
y=r\sin (\theta) to obtain:


r^2\cos^2\theta-r^2\sin^2\theta=4

This implies that:


r^2(\cos^2\theta-\sin^2\theta)=4

Apply double angle identity to obtain:


r^2\cos 2\theta=4

This implies that:


r^2=(4)/(\cos 2\theta)

This simplifies to:


r^2=4\sec 2\theta}

User Anders Rune Jensen
by
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