# How would you determine the equation of the circle which passes through the points D(-5,-5), E(-5,15), F(15,15)?

##### 2 Answers

Substitute each point to the equation of the circle, develop 3 equations, and substract the ones that have at least 1 coordinate common (

Answer is:

#### Explanation:

The equation of the circle:

Where

Substitute for each given point:

**Point D**

**(Equation 1)**

**Point E**

**(Equation 2)**

**Point F**

**(Equation 3)**

**Substract equations #(1)-(2)#**

**Substract equations #(2)-(3)#**

Now that

So the equation of the circle becomes:

The circle's equation is

#### Explanation:

First we need to find the equation of two lines, each one perpendicular to the segments formed by a pair of the given points and passing through the midpoint of this pair of points.

Since points D and E (

Equation of Line DE, where

Equation of line 1 perpendicular to DE and passing through midpoint

line 1

Equation of Line EF, where

Equation of line 2 perpendicular to EF and passing through midpoint

line 2

Combining equations of lines 1 and 2 (

The distance between point C to any of the given points is equal to the circle's radius

In the formula of the equation of the circle: