A circle has a center that falls on the line #y = 1/4x +2 # and passes through # ( 3 ,7 )# and #(7 ,1 )#. What is the equation of the circle?
1 Answer
Explanation:
The Cartesian form for the equation of a circle is:
where
We can use the two points,
Expand the squares:
Subtract equation [3.1] from equation [2.1]:
Evaluate the given line at the point
Substitute equation [5] into equation [4]:
Use equation [5] to solve for k:
Use equation [2] to find the value of r:
Substitute the know values into equation [1]: