The equation of a circle is given by

, where is the centre and is the radius.

From the information given, we can generate three equations in three unknowns, so that we can solve them simultaneously for and .

Substituting point A into the equation gives

.

Substituting point B into the equation gives

.

This circle's derivative is given by:

.

This is the derivative, which gives us the gradient of the tangent at all points on the circle.

If it's tangent at B is the line , we can rearrange this to read .

So the gradient of the tangent at point B is .

So at point the gradient is .

Substituting these values into the derivative gives

.

We can now solve for and .

So far we have:

and .

Therefore

.

We also know:

, so

.

Finally, we know that

.

Now we finally have enough information for the equation of the circle:

.