Question

How do you convert `x^2 -4y^2 =4` to polar form?

Answer 1

`r^2=4/(cos^2theta-4sin^2theta)`

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)|)))`

`rArrx^2-4y^2=4rArr(rcostheta)^2-4(rsintheta)^2=4`

`rArrr^2cos^2theta-4r^2sin^2theta=4`

`rArrr^2(cos^2theta-4sin^2theta)=4rArrr^2=4/(cos^2theta-4sin^2theta)`