A circle has a center that falls on the line #y = 8/7x +6 # and passes through # ( 2 ,1 )# and #(3 ,6 )#. What is the equation of the circle?
1 Answer
Explanation:
The standard equation of a circle is
where
Therefore, the given equation of a the line at the center point is:
The standard equation evaluated at the two given points gives us the two equations:
There are 3 equations and 3 unknown values.
We can temporarily eliminate the variable, r, by setting the left side of equation [2] equal to the left side of equation [3]:
Using the pattern,
Cancel the square terms:
Combine the constant terms into a single term on the right:
Combine the h terms into a single term on the right:
Combine the k terms into a single term on the left:
Divide both sides by 10:
Subtract equation [4] from equation [1]:
Substitute this value for h into equation [1]:
Substitute these value for h and k into equation [2]:
Check with equation [3]:
This checks