# A circle has a center that falls on the line #y = 2/3x +1 # and passes through #(5 ,2 )# and #(3 ,2 )#. What is the equation of the circle?

##### 1 Answer

Aug 21, 2016

#### Explanation:

The general equation of a circle is

Where (a,b) is the centre of the circle and r is the radius.

So (a,b) is on the line y=

Substituting b=

(5,2) is on the circle so

(3,2) is on the circle so

Subtract equation 3 from equation 2 gives

Multiply out and simplify gives a= 4

Substitute in equation 1 gives b=

Substitute in equation 2 gives

Put all values into equation 3 as a check.

Yes it is correct