# Given #C_1->y^2+x^2-4x-6y+9=0#, #C_2->y^2+x^2+10x-16y+85=0# and #L_1->x+2y+15=0#, determine #C->(x-x_0)^2+(y-y_0)^2-r^2=0# tangent to #C_1,C_2# and #L_1#?

##### 1 Answer

There are two solutions as explained below.

#### Explanation:

Firstly we will represent the geometric objects in a more convenient formulation.

So

After reduction, we have

Now, given

find

such that

Here

We can stablish the following retationships

if

where

Finally we get the following equations

so we have four equations and four incognitas

Solving we obtain

Attached the figure with the solutions in red and the initial geometric elements in black.