SOLUTION: A straight line 2x-y+1=0 touches the circle on the point (2,3) and the centre of circle situated on the line x+y=9. find the eqation of the circle.

Algebra ->  Circles -> SOLUTION: A straight line 2x-y+1=0 touches the circle on the point (2,3) and the centre of circle situated on the line x+y=9. find the eqation of the circle.      Log On


   

Question 971370: A straight line 2x-y+1=0 touches the circle on the point (2,3) and the centre of circle situated on the line x+y=9. find the eqation of the circle.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This response is not a full solution.

Line of tangency is also y=2x+1;
Line containing center is also y=-x+9;

Try to sketch as much of the graph as you can do.

There is a line with slope -1%2F2 through point (2,3) which intersects with the line y=-x+9. That intersection point is the center of the circle.

Distance from (2,3) to the center point of circle gives the size of the radius.