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 ...

Find the equation of the tangent to the circle \(x^2 + y^2 = 25 \) at the point (3, -4). The tangent will have an equation in the form \(y = mx + c\) so to find the equation you need to find the ...