# Question #de290

##### 2 Answers

#(x-4)^2 +(y+5)^2 =36= 6^2

#### Explanation:

Rewrite as

You complete the squares, using the patterns:

and

#### Explanation:

The standard form for the equation of a circle is:

where x and y correspond to any point,

Given:

Move the x terms together, the y terms together, and the constant to the right:

We want to make the first 3 terms in equation [4] look like the right side of equation [1] so we insert an

The first 3 terms of equation [5] look like the right side of equation [1].

We can match the

Find the value of h by dividing both sides of the equation by -2x:

This means that, in equation [5], we can replace the terms

We want to make the y terms in equation [6] look like the right side of equation [2} so we add a

The y terms on the left of equation [7] look like the right side of equation [2].

Match the

Find the value of k by dividing both sides by -2y:

This means that, in equation [7], we can replace

Simplify the constants on the right:

Write the constant as a square:

This is a circle with a radius of 6 and a center at