(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

On the circles y^2+x^2=1 and y^2+(x-3)^2=4

There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle.

2. Relevant equations

the derivative of the first circle i found:

y'=-x/y

the derivative of the second cirlce I found:

y'=-2x+6/2y

and also

x^2+y^2=1

3. The attempt at a solution

so I have these equations for slopes:

-x_{1}/y_{1}

-2x_{2}+6/2y_{2}

y_{2}-y_{1}/x_{2}-x_{1}

Now where do I go from here, can someone get me started with the rearranging or whatever?

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# Homework Help: Points where tangent line touches 2 circles

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