The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form \(y = mx + c\).

Where does this formula come from? One method of obtaining this equation is to integrate dxdy over the area of a circle. Well, you probably wouldn't want to do that in cartesian coordinates - but ...

4. Equation of tangent to a circle, 5. Equation of normal to a circle, 6. Equation of a circle passing through a line and touching a line, 7. Length of tangent from an external point, 8.

The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form \(y = mx + c\).