Question

How do you convert `x^2-y^2=1` to polar form?

Answer 1

`r^2=sec2theta`

Explanation:

To convert from `color(blue)"cartesian to polar"` use the following.

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

We will also make use of the identities.

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos2theta=cos^2theta-sin^2theta)color(white)(a/a)|)))`

and `color(red)(|bar(ul(color(white)(a/a)color(black)(sectheta=1/(costheta))color(white)(a/a)|)))`

Using the conversion formulae above we can write.

`x^2-y^2=1rArr(rcostheta)^2-(rsintheta)^2=1`

`rArrr^2cos^2theta-r^2sin^2theta=1`

`rArrr^2(cos^2theta-sin^2theta)=1rArrr^2=1/(cos^2theta-sin^2theta)`

`rArrr^2=1/(cos2theta)=sec2theta`