1. The problem statement, all variables and given/known data Find the points of tangency to a circle given by x^2+y^2=9 from point (12,9). 2. Relevant equations dy/dx=-x/y (what I've been able to come up so far) 3. The attempt at a solution Taking the derivative I got dy/dx=-x/y Let the unknown point of tangency be (a,b) y-b=(-a/b)(x-a) Simplifying that, I got: by-ax=a^2+b^2 a and b fall on the circle; the circle's equation is x^2+y^2=9; therefore, a^2+b^2=9 by-ax=9 (12,9) is a point on this ^ line, so 9b-12a=9 b=(4/3)a+1 Substituting back into the original equation x^2+y^2=9, a^2+((4/3)a+1)^2=9 Simplifying that got me 25a^2+27a-72=0. This was the point where I knew I was wrong. Where did I go wrong/how do I fix it?