SOLUTION: Show that the circles and x^2 + y^2 -16x -12y +75 = 0 and 5x^2 +5y^2 -32x - 24y +75 = 0 touch each other and find the equation of the common tangent at their point of contact.

Question 868571: Show that the circles and x^2 + y^2 -16x -12y +75 = 0 and 5x^2 +5y^2 -32x - 24y +75 = 0 touch each other and find the equation of the common tangent at their point of contact.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The process for how to get the intersection point is this:

Convert each equation to standard form using Completing The Square. Solve each standard form equation for y. Equate the two expressions for y, and solve for x. Use the value found for x in either equation to compute the value for y. You now would have the (x,y) point of intersection.

The process to get the equation of the tangent line through that found point is to use the two centers of the circles. Find the equation for the line through the found intersection point which is perpendicular to the line containing the two centers (which is a very common coordinate geometry exercise).
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