Question

Given the equation `2x^2+2y^2+24x-81=0?`

Find the center and radius of a circle

Answer 1

Center is `(-6,0)` and radius is `8.746`

Explanation:

`2x^2+2y^2+24x-81=0` can be written as (dividing each term by `2`)

`x^2+y^2+12x-81/2=0`

or `x^2+2xx x xx6+6^2+y^2-6^2-81/2=0`

or `(x+6)^2+y^2=81/2+36=153/2`

or `(x-(-6))^2+(y-0)^2=(sqrt(153/2))^2`

which is locus of a point which moves so that

its distance from `(-6,0)` is always `sqrt(153/2)=8.746`

Hence, center is `(-6,0)` and radius is `8.746`
graph{2x^2+2y^2+24x-81=0 [-20, 20, -10, 10]}