Convert the rectangular equation to a polar equation.

y^2-x^2=7sqrt(x^2+y^2)

Question

Convert the rectangular equation to a polar equation.

y^2-x^2=7sqrt(x^2+y^2)

tkhunny · Answer

$x = r\cos(\theta)$
$y = r\sin(\theta)$

Substitute and Simplify.

anonymous · Answer

i know that.. but what i got was -rcos(2theta) = 7r
and it says the answer is r=-7/cos(2theta)

tkhunny · Answer

Why didn't you say so?  If you show your work, we can have a much better conversation much more quickly.

$x^{2} = r^{2}\cos^{2}(\theta)$

$y^{2} = r^{2}\sin^{2}(\theta)$

$\sqrt{x^{2} + y^{2}} = r$

And we're left with: $r(\sin^{2}(x) - cos^{2}(x)) = 7$

Sure enough, exctly as you have it.  So, what's the dilemma?  Not the form allowed by the exam?  Try cos(x) = 1/sec(x)