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

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


   

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(39621) About Me  (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).


sqrt%28%281%29%5E2%2B%28y%2B1%29%5E2%29=sqrt%28%285%29%5E2%2B%28y-1%29%5E2%29
sqrt%281%2B%28y%2B1%29%5E2%29=sqrt%2825%2B%28y-1%29%5E2%29
1%2By%5E2%2B2y%2B1=25%2By%5E2-2y%2B1
1%2B2y%2B1=25-2y%2B1
4y%2B1%2B1=25%2B1
4y=24
highlight%28y=6%29

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 r%5E2,
which you would determine using either of the given points.
What is r%5E2?
highlight_green%28x%5E2%2B%28y-6%29%5E2=r%5E2%29----substitute either of the given points and find.