You need both a point and the gradient to find its equation. You are usually given the point - it's where the tangent meets the circle. To find the gradient use the fact that the tangent is ...

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. The gradient of the ...