Question

Line L is tangent to a circle whose center is at (3,2). If the point of tangency is (6,6) what is the slope of line L?

Answer 1

Slope of the line L will be
`-(3)/(4)`

Explanation:

We will use the theorem that tangent to a circle is always perpendicular to the radius joining center of the circle and point of tangency.

Let
`m_(1)` is the slope of line joining center of the circle (3, 2) and point of tangency (6, 6).

And
`m_(2)` is the slope of line L.

Then by the fact given above
`m_(1)* m_(2)=-1`-----(1)

Now
`m_(1)=(y-y')/(x-x')`

`m_(1)=(6-2)/(6-3)`

`m_(1)=(4)/(3)`

Now from the equation 1

`(4)/(3)* m_(2)=-1`

`m_(2)=-(3)/(4)`

Therefore, slope of the line L will be
`-(3)/(4)`