The equation of the circle is:

rewrite the line as:

Now substiture this for in the equation of the circle:

which simplifies down to:

.

Now that the line is a tangent to the circle means that there is only one

point where they meet which corresponds to a double root of the quadratic.

The quadratic has a double root when the discriminant is zero, ie:

which is a quadratic in . This has roots ,

and as must be positive the root we require is .

So the equation of the circle is:

RonL