Draw the circle and mark the point of the circle center that is at a = R and b (because the circle is tangent to the y axis, b is unknown)


We can write the equation of the circle related to the points and the center of the circle:
( x_{1} − R )^{2} + ( y_{1} − b )^{2} = R^{2} 
(1) 
( x_{2} − R )^{2} + ( y_{2} − b )^{2} = R^{2} 
(2) 
From first eq. (1) 
x_{1}^{2} − 2x_{1}R + R^{2} + y_{1}^{2} − 2y_{1}b + b^{2} = R^{2} 

x_{1}^{2} − 2x_{1}R + y_{1}^{2} − 2y_{1}b + b^{2} = 0 


From first eq. (2) 
x_{2}^{2} − 2x_{2}R + R^{2} + y_{2}^{2} − 2y_{2}b + b^{2} = R^{2} 

x_{2}^{2} − 2x_{2}R + y_{2}^{2} − 2y_{2}b + b^{2} = 0 
Substitute R from eq. (3) into the last equation and arrange terms:
b^{2}(2x_{1} − 2x_{2}) + b(4x_{2}y_{1} − 4x_{1}y_{2}) + 2x_{1}x_{2}^{2} − 2x_{1}^{2}x_{2} + 2x_{1}y_{2}^{2} − 2x_{2}y_{1}^{2} = 0
b^{2}(x_{1} − x_{2}) + b(2x_{2}y_{1} − 2x_{1}y_{2}) + x_{1}x_{2}^{2} − x_{1}^{2}x_{2} + x_{1}y_{2}^{2} − x_{2}y_{1}^{2} = 0
We get a quadratic equation with the unknown b (all the points are given) the solution is:
Now insert the value of b into eq. (3) to get the radius R of the circle.
Insert the given values of the points (6 , 2) and (3 , − 1) to get b:
The radius from eq. (3) for b = 2 is: 

And the second radius for b = − 10 is: 

We can see that there are two circles that fulfills the requirements of the given data.
The two circles centers are at the points (3 , 2) and (15 , − 10)
