# How do you find an equation of the circle that satisfies the given conditions: endpoints of a diameter are P(−1, 2) and Q(7, 8)?

##### 2 Answers

#### Explanation:

The coordinates of the centre of the circle will be the coordinates of the midpoint of the diameter.

We next find the length of the diameter using the distance formula:

This is the length of the diameter, so radius is:

The equation of a circle is given as:

Where

#### Explanation:

Equation of a circle is of the form:

Where (a,b) represents the co ordinates of the circle's centre

And 'r', the circle's radius

Equation to find the coordinates of the centre of a line segment is

=

Hence,

( 0.5 ( -1 + 7 ) ) , ( 0.5 ( 2 + 8 ) )

= ( 3 , 5 )

For the distance between two points ,

Hence,

= 10

Diameter of circle = 10

Radius , r = 5

=

=