# Given a circle with equation #x^2+(y-1)^2 = 10#, what are the equations of the two tangents to the circle that run through the point #(4, -1)# ?

##### 1 Answer

#### Explanation:

This question is not quite as mean as it appears at first glance.

The points where the tangents touch the circle are

The geometry largely concerns right angled triangles with sides

For example, the radial line segment from

The line through

#y = -3x+11#

The line through

#y = 1/3x-7/3#

In both of these cases, calculate the slope (the coefficient of the

graph{(x^2+(y-1)^2-10)(x^2+(y-1)^2-0.02)((x-4)^2+(y+1)^2-0.02)(y+3x-11)(y-1/3x+7/3)((x-3)^2+(y-2)^2-0.02)((x-1)^2+(y+2)^2-0.02) = 0 [-10, 10, -5, 5]}