SOLUTION: Find the equation of the circle that passes through (1,-1) and (5,1) and has its centre on the y axis.

Question 917304: Find the equation of the circle that passes through (1,-1) and (5,1) and has its centre on the y axis.
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Harder than your other question because this one uses a tilted chord for the two given points.

The y axis has a general point (0,y) which will be the center of your circle. You do not
know the value of this y. The distance from y to each of the given points is the same.

D from (1,-1) to (0,y) is equal to D from (5,1) to (0,y).

You know from that the center of the circle is (0,6);
You should be able to form a standard-form equation of the circle, and the right side member is ,
which you would determine using either of the given points.
What is ?
----substitute either of the given points and find.

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