University of South Carolina High School Math Contest/1993 Exam/Problem 25
Problem
What is the center of the circle passing through the point and tangent to the circle
at
? (Two circles are tangent at a point
if they intersect at
and at no other point.)
![$\mathrm{(A) \ }(0,-6) \qquad \mathrm{(B) \ } (1,-9) \qquad \mathrm{(C) \ } (-1,-9) \qquad \mathrm{(D) \ } (0,-9) \qquad \mathrm{(E) \ } \rm{none \ } \rm{of \ } \rm{these}$](http://latex.artofproblemsolving.com/0/0/b/00bc059af7b25de3ab7957a6c887569ef06b1fdd.png)
Solution
Let the circle we are looking for be where
is the center. Plugging in points
and
gives us that
. Seeing our answer choices, none of the points work, thus our answer is E.