Question

How do you find the standard form of the equation of the circle with center at origin with points (-2,3)?

Answer 1

`x^2+y^2=13`

Explanation:

Any circle centred at `(a,b)` and having radius `r` has equation
`(x-a)^2+(y-b)^2=r^2`

So in this case the centre is `(0,0)` and the radius may be found from the given point and Pythagoras as `r^2=x^2+y^2=2^2+3^2=13`.

Hence the equation is `x^2+y^2=13`.