How do you convert $-y+2=(3x+4)^2+(y-1)^2$ into polar form?

Question

1423 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-01T12:20:10

Given that $-y+2=(3x+4)^2+(y-1)^2$

Substituting $x=r\cos\theta$ & $y=r\sin\theta$

$-r\sin\theta+2=(3r\cos\theta+4)^2+(r\sin\theta-1)^2$

$-r\sin\theta+2=9r^2\cos^2\theta+16+24r\cos\theta+r^2\sin^2\theta+1-2r\sin\theta$

$(8\cos^2\theta+1)r^2+(24\cos\theta-\sin\theta)r+15=0$

How do you convert -y+2=(3x+4)^2+(y-1)^2-y+2=(3x+4)^2+(y-1)^2 into polar form?