Question

How do you write the standard from of the equation of the circle given center (-2, 4) and radius 7?

Answer 1

`(x+2)^2 +(y-4)^2 =49`

Explanation:

The standard or general form of a circle is
`(x-h)^2 +(y-k)^2 = r^2`

where `(h,k)` is the center of the circle and `r` is the radius.

In this problem, `h=-2`, `k=4` and `r=7`

Plugging these values into the equation gives:

`(x- -2)^2 +(y-4)^2 =7^2`

`(x+2)^2 +(y-4)^2 =49`

Some teachers refer to the "standard form" as the equation resulting from squaring the binomials and gathering all terms on one side. This is uncommon, but here it is.

`(x+2)(x+2) +(y-4)(y-4)=49`

`x^2 +4x +4 +y^2 -8y +16=49`

Rearranging and combining the constant terms gives

`x^2 +y^2+4x-8y-29=0`