# What are the center and radius of the circle defined by the equation #x^2+y^2-6x+8y+21=0#?

##### 2 Answers

The center is

#### Explanation:

We need

Let's rearrange the equation as

We can now complete the squares

We can now factorise

This is the equaton of a circle, center

graph{(x-3)^2+(y+4)^2-4=0 [-6.42, 9.38, -7.07, 0.83]}

Center is

#### Explanation:

or

or

or

This is the locus of a point which moves so that its distance from point

Hence this is the equation of a circle whose center is

graph{x^2+y^2-6x+8y+21=0 [-2.043, 7.957, -6.12, -1.12]}