Question

How do you convert `r = 1/(4 - cosΘ)` to rectangular form?

Answer 1

In rectangular form : `15x^2+16y^2 -2x =1`

Explanation:

We know, the connecton between poar & catesian coordinates as `r^2=x^2+y^2 ; x=r cos theta ;y=r sin theta ; tan theta =y/x`

`r= 1/(4-cos theta) = 1/(4-x/r) = r/(4r-x) or 4r-x= cancelr/cancelr or 4r=x+1 or 4*sqrt(x^2+y^2) = x+1 or 16 (x^2+y^2) = (x+1)^2 or 15x^2+16y^2 -2x =1`
In rectangular form : `15x^2+16y^2 -2x =1` [Ans]