Question

convert from regular form to polar form
x^2 + xy + y^2 = 1

Answer 1

Use the conversions:
\[x=r\cos\theta\\
y=r\sin\theta\]

Answer 2

I did and when I do I end up getting
r^2 + r(cos(theta)sin(theta)) = 1
and I don't know where to go from here or if that's even right

Answer 3

\[x^2+xy+y^2=1\\
(r\cos\theta)^2+(r\cos\theta)(r\sin\theta)+(r\sin\theta)^2=1\\
r^2\cos^2\theta+r^2\cos\theta\sin\theta+r^2\sin^2\theta=1\\
r^2\left(\cos^2\theta+\sin^2\theta +\cos\theta\sin\theta\right)=1\]
Do you see what you can do with this?

Answer 4

wouldn't you combine cos^2(theta) + sin^2(theta) to = 1

Answer 5

Yep, that's right. So you have
\[r^2\left(1+\cos\theta\sin\theta\right)=1\]

Answer 6

so what would be the next step?

Answer 7

Solve for r. Or rather, r².