A circle has a center that falls on the line #y = 3/2x +1 # and passes through #(1 ,2 )# and #(6 ,1 )#. What is the equation of the circle?
1 Answer
The equation of the circle is:
Explanation:
The equation of a circle is:
where
Substitute the point (h,k) into the equation for the line on which the center lies:
We can use the two given points and the equation of a circle to write two more equations:
We can, temporarily, eliminate the variable r by setting the left side of equation [2] equal to the left side of equation [3]:
Use the pattern
The square terms are the same on both sides of the equation, therefore, they cancel:
Collect the 4 constant terms into a single term on the right:
Collect the 2 h terms into a single term on the right:
Collect the 2 k terms into a single term on the left:
Divide both sides by -2:
Subtract equation [4] from equation [1]:
Substitute 34/7 for h in equation [1]:
Substitute the values for h and k into equation [2] or [3] (I will use equation [2]):
The equation of the circle is: