Question

Write the equation with rectangular coordinates.
r^2=6cos(2theta)
(x2 + y2)2 =

Answer 1

Hmmmm

Answer 2

So you're trying to solve for \(\Large\rm (x^2+y^2)^2\) ?
Weird :U
Ok ok ok ok ok here is what I'm thinkin...

Answer 3

\[\Large\rm r^2=6\cos(2\theta)\]Multiply both sides by r^2,\[\Large\rm (r^2)^2=6r^2 \cos(2\theta)\]Rewrite the right side using our Cosine Double Angle Identity:\[\Large\rm (r^2)^2=6r^2(\cos^2\theta-\sin^2\theta)\]Distribute the r^2,\[\Large\rm (r^2)^2=6r^2\cos^2\theta-6r^2\sin^2\theta\]

Answer 4

Then use our things for converting from polar to rectangular:\[\Large\rm x=r \cos \theta, \qquad y=r \sin \theta\]

Answer 5

Giving us,\[\Large\rm (x^2+y^2)^2=6x^2-6y^2\]Something like that I guess....?

Answer 6

wow sorry i hadnt seen that someone had responded

Answer 7

wow
thank you