A circle has a center that falls on the line #y = 2/9x +4 # and passes through # ( 3 ,1 )# and #(5 ,7 )#. What is the equation of the circle?
1 Answer
Explanation:
The equation for a circle:
where
Use equation [1] and the two given points to write two equations:
Substitute h for x and k for y in the given equation:
Multiply both sides of the equation by 9:
Write in standard form:
Because
Expand the squares, using the pattern
The
Combine all of the constant terms into a single term on the right:
Combine the h terms and the k terms on the left:
Divide both sides of the equation by 4:
Here are the two equations that define the values of h and k:
Multiply equation [5] by 3 and add to equation [4]:
Substitute
To find the value of r, substitute the value for h and k into equation [3]:
Substitute these values into equation [1]: