Question

How do you find the center and radius of the circle given `x^2+y^2-3x+8y=20`?

Answer 1

The center is `(3/2,-4)`
The radius is `=6.185`

Explanation:

We have to rearrange the equation and complete the squares

`x^2+y^2-3x+8y=20`

`x^2-3x+y^2+8y=20`

`x^2-3x+9/4+y^2+8y+16=20+9/4+16`

`(x-3/2)^2+(y+4)^2=38.25=6.185^2`

So the center of the circle is `(3/2,-4)`
and the radius is `=6.185`

graph{x^2+y^2-3x+8y=20 [-14.28, 14.2, -10.85, 3.39]}