Example Find the equation of the tangent to the circle x 2 + y 2 2 x 2 y 23 = 0 at the point P (5, 2) which lies on the circle. The centre of the circle is (1, 1) m C P = 2 1 5 1 = 3 4 ...

First, find m, the gradient of the tangent. On a diagram, draw the circle and the tangent at the point P (3, -4) and draw the radius from the centre (0, 0) to the point P.