# Example of Tangents Drawn from a Point to the Circle

We will find the equation of tangent lines drawn from the point to the circle given by

Now to solve this example we follow these steps.

Consider the given equation of a circle

Compare this circle with the general equation of a circle as

Here we have the following values

Now the center of the circle (i) is

The radius of the circle (i) is

Let be the slope of the tangent drawn from to the given circle (i), then its equation is

Since the line (ii) is a tangent to the circle (i), so the distance of the centre of the circle should be equal to its radius, i.e.:

Now solving this quadratic equation of variable , using the quadratic formula we have

Putting the value of one root, , in equation (ii) we get

This is the first equation of the required tangents to the circle.

Putting the value of the second root, , in equation (ii) we get

This is the second equation of the required tangents to the circle.