Suppose that there is only one value of x for which the distance from (5,6) to (3x-7,ax+2) is 4. If a≠0 what is a?
+600 $(3x-12)^2+(ax-4)^2=16\implies 9x^2-72x+144+a^2x^2-8ax+16=16\implies (9+a^2)x^2-(72+8a)x+144=0$.
Discriminant is zero, so $(72+8a)^2=4(144)(9+a^2)\implies a=\boxed{\frac{9}{4}}$.
