Question

How do you convert `6y= 5x-2` into a polar equation?

Answer 1

`r=-2/(6sintheta-5costheta)`

Explanation:

To convert from `color(blue)"Cartesian to Polar form"`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta,y=rsintheta)color(white)(a/a)|)))`

Substitute in Cartesian equation

`rArr6y=5x-2rArr6(rsintheta)=5(rcostheta)-2`

`rArr6rsintheta-5rcostheta=-2`

`rArrr(6sintheta-5costheta)=-2`

`rArrr=-2/(6sintheta-5costheta)" in Polar form"`