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 ...

This means that, using Pythagoras’ theorem, the equation of a circle with radius \(r\) and centre (0, 0) is given by the formula \(x^2+ y^2= r^2\). Find the equation of a circle with radius 3 ...