# How do you find the center and radius for #x^2 + y^2 - 6x - 4y - 12 = 0#?

##### 2 Answers

Use the quadratic 'Complete the Square' method

#### Explanation:

#x^2 - 6x +y^2 - 4y = 12

Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides.

#x^2 -6x + 9 + y^2 - 4y + 4 = 12 + 9 + 4

(x - 3)^2 + (y -2)^2 = 25

Circle centered at (3,2) with radius = 5

Center:

#### Explanation:

An equation in the form:

is the standard form for the equation of a circle with center

Lets try to convert the given equation:

into the standard form for the equation of a circle.

Group the

Complete the square for each of

Write the left side as the sum of two squared binomials

and simplify the result on the right side

Express the right side as a square.

...the equation for a circle with center