Question

How do you convert `x^2+y^2 - 2y=0` to polar form?

Answer 1

`r=2sintheta`

Explanation:

Using the formulae that link Cartesian to Polar coordinates.

`• x = rcostheta" and "y=rsintheta`

and substituting into the given equation

`rArr(rcostheta)^2+(rsintheta)^2-2rsintheta=0`

expanding brackets to obtain.

`r^2cos^2theta+r^2sin^2theta=2rsintheta`

Take out a common factor of `r^2`

`rArrr^2(cos^2theta+sin^2theta)=2rsintheta`

using the trig. identity `color(red)(|bar(ul(color(white)(a/a)color(black)(cos^2theta+sin^2theta=1)color(white)(a/a)|)))`

`rArrr^2=2rsintheta`

divide both sides by r

`rArrr=2sintheta`