Question

How can we write rectangular equations `3x^2+4y=1` and `x^2-4y=4` in polar form?

Answer 1

`3r^2cos^2theta+4rsintheta=1` and `r^2cos^2theta-4rsintheta=4`

Explanation:

The relation between polarcoordinates `(r,theta)` and Cartesian coordinates `(x,y)` is given by `x=rcostheta` and `y=rsintheta`

Therefore we can write `3x^2+4y=1` as

`3r^2cos^2theta+4rsintheta=1`

and `x^2-4y=4` as

`r^2cos^2theta-4rsintheta=4`