# How do you write the equation for a circle where the points passes through the points (1,1), (-2, 2), and (-5,1)?

##### 1 Answer

#### Answer:

Please see the explanation for the steps leading to:

#### Explanation:

Use the standard form for the equation of a circle:

And the points,

To write 3 equations:

Temporarily eliminate the variable r by setting the left side of equation [1] equal to the left side of equation [2] and the same for equation [1] and equation [3]:

Please notice that equation [4] has

Use the pattern

The

Use equation 6 to solve for h:

Combine like tems of equation [5] with k terms on the left and constant and h terms on the right:

Substitute -2 for h:

Substitute the values for h and k into one of the first three equations (I will use equation [2]):

Solve for r:

The equation of the circle is: