Question

How do you convert `x^2+y^2=9` to polar form?

Answer 1

`r^2=9`

Explanation:

Using the formulae that links Cartesian to Polar coordinates.

`•x=rcostheta" and " y=rsintheta`

Substitute these values into the equation.

`rArr(rcostheta)^2+(rsintheta)^2=9`

`rArrr^2cos^2theta+r^2sin^2theta=9`

remove common factor of `r^2`

`rArrr^2(cos^2theta+sin^2theta)=9`

Using the trig. identity: `cos^2theta+sin^2theta=1`

`rArrr^2=9`