Question

How do you find the center and radius of the circle given `x^2+y^2+2x+4y=9`?

Answer 1

The center is `(-1,-2)` and the radius is `sqrt14=3.74`

Explanation:

The equation of a circle, center, `(a,b)`and radius `r` is,

`(x-a)^2+(y-b)^2=r^2`

Let's complete the squares in the above equation

`x^2+2x+y^2+4y=9`

`x^2+2x+1+y^2+4y+4=9+1+4`

`(x+1)^2+(y+2)^2=(sqrt14)^2`