Question

How do you find the center and radius of the circle `x^2+y^2+6x-8y-135=0`?

Answer 1

Centre (-3,4) r=12.64911064

Explanation:

`(x-a)^2+(y-b)^2=r^2` is the general formula for a circle so rearrange the equation and then complete the square.

`x^2+6x+y^2-8y=135`

`(x+3)^2-9+(y-4)^2-16=135`

`(x+3)^2+(y-4)^2-25=135`

`(x+3)^2+(y-4)^2=160`

`a=-3, b=4 and r=sqrt160`