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?
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=
(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