# Equation of a Tangent Line from a Point on the Circle

How to find the equation of a tangent line from a point on the circle: example and its solution.

## Example

Draw a radius that meets the tangent line at *P*(3, 1):*OP*.

Find the slope of *OP*:*m*_{OP} = 1/3.

*OP* and the tangent line are perpendicular.

Tangent to a circle

So (*m*, slope of the tangent)⋅(1/3) = -1

Perpendicular lines

So *m* = -3.

And the tangent line passes through *P*(3, 1).

Then *y* - 1 = -3(*x* - 3).

Point-slope form