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## Homework Statement

Show that the line 2x+3y=27 is a tangent to the circle with centre (4,2) and radius sqrt of 13. Find the co-ordinates of the point of contact. (Without a calculator)

## Homework Equations

## The Attempt at a Solution

I have worked out that the equation of the circle is (x-4)^2 + (y-2)^2=13.

I have tryed to substitute in values of x and y from the equation of the tangent to try and work out the discriminant but I haven't been able to create an equation with just either Xs or Ys in that is easy to work out the disccriminant of without using a calculator. Please show me the method for both parts of the question.