Question

How do you find the center and radius of the circle given `4x^2+4y^2+36y+5=0`?

Answer 1

The centre of the circle is `(0,-9/2)` and the radius `=sqrt19`

Explanation:

We complete the squares

`4x^2+4y^2+36y+5=0`

`4x^2+4(y^2+9y)=-5`

`4x^2+4(y^2+9y+81/4)=-5+81`

`4x^2+4(y+9/2)^2=76`

Dividing by `4`

`x^2+(y+9/2)^2=76/4=19`

So the centre of the circle is `(0,-9/2)` and the radius `=sqrt19`
graph{4x^2+4y^2+36y+5=0 [-13.72, 14.76, -13.18, 1.07]}