Question

Which equation represents the polar form of x2 + (y – 6)2 = 36?

Answer 1

`r^2-12r\sin\theta=1`

Step-by-step explanation:

We need to write the polar form of the given equation :

`x^2+(y-6)^2=36`

Put
`x=r\cos\theta` and
`y=r\sin\theta`

`x^2+(y-6)^2=36\\\\(r\cos\theta)^2+(r\sin\theta-6)^2=36\\\\r^2\cos^2\theta+r^2\sin^2\theta+36-12r\sin\theta=36\ \ [\because (a-b)^2=a^2+b^2-2ab]\\\\r^2(\cos^2\theta+\sin^2\theta)-12r\sin\theta=0\\\\\text{We know that}, \cos^2\theta+\sin^2\theta=1\\\\r^2-12r\sin\theta=1`

Hence, the above is the polar form of the given equation i.e.
`r^2-12r\sin\theta=1`