Math Forum :: View topic – CIRCLES ………..URGENT…………..

For 1), Basically you need 3 independent relations about a,b,c to find them all. they are (1) (1,c) lies on the line (2) (1,c) lies on the circle (3) The line is tangent to the circle Can you omit one of them? Are they independent? (Think about the picture!) Since the line and the circle touch at exactly one point, the system of 2 equations (with unkowns x and y) has exactly one solution. (why?) Eliminating one of the unkowns, say y, we have now a quadratic equation in x. This equation has only one root because there is only one point of intersection. (The solution of this quadratic equation is the x-coordinate of the point of intersection)

Thus the discriminant is 0, which gives you the third relation about a,b,c.