The question is as follows:
The circle $x^2-6x+y^2-8y=24$ is transformed through a dilation into $x^2-14x+y^2-4y=-44$, point by point. The circles have two common external tangent lines, which meet at the dilation center. Find the size of the angle formed by these lines, and write an equation for each line.
I used Desmos to create the two circles. The center and radius for the original circle is $(3, 4)$ and $1$, respectively. The center and radius for the image circle is $(7,2)$ and $3$, respectively.
I know that one of the lines' equation has to be $y=5$. But I am not sure about the other one. Also, I have no idea about how I can calculate the angle created by the external tangent lines.
Any help will be greatly appreciated!