# How do you find the equations of the two tangents to the circle #x^2 + y^2 - 2x - 6y + 6 = 0# which pass through the point P(-1,2)?

##### 2 Answers

#### Explanation:

Given equation of circle:

The above circle has center at

Let tangent passing through the point

Now, the line joining points

Now, subtracting (2) from (1) we get

Substituting

Substituting the values of

Hence, the points at which tangents are drawn are

Now, the equation of tangent line joining

Similarly, the equation of tangent line joining

hence, the equations of tangent lines drawn from the external point to the given circle are

#### Explanation:

Let us solve the **Problem** using **Geometry.**

For this, we suppose that the **point of contact** of the **required**

**tangent** through **circle**

**centre** is

From **Geometry,** we know that,

Hence,

Also,

Then, by

Thus, there are **two tangents** through

at

Their eqns. are,