# A circle has a center that falls on the line #y = 1/3x +7 # and passes through # ( 3 ,1 )# and #(7 ,9 )#. What is the equation of the circle?

The equation of the circle is:

Use the standard Cartesian form of the equation of a circle

and the two points to write two equations:

Expand the squares:

Subtract equation [2.1] from equation [1.1]

Combine like terms:

Divide both sides by 8:

Use equation [4] to find the value of k:

Substitute the values of h and k into equation [1]:

Substitute the values for h, k and r into the standard form:

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The equation of the circle is ( (x - 5)^2 + (y - 5)^2 = 10 ).

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