Question

How do you write a polar equation for the circle centered at the origin with radius `sqrt2`?

Answer 1

`r^2=2`

Explanation:

The equation of a circle centred at the origin is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(x^2+y^2=r^2)color(white)(2/2)|)))`
where r is the radius.

`x^2+y^2=(sqrt2)^2`

`rArrx^2+y^2=2larr" equation in cartesian form"`

To convert from `color(blue)" cartesian to polar form"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt(x^2+y^2))color(white)(2/2)|)))`

`rArrx^2+y^2=2tor^2=2larr" in polar form"`