Subject: Common Tangents - Calculus Name: Anne Who is asking: Student Level: Secondary Question: I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x2 and 2y=-x2-16 Thanks for the help. :) Hi Anne, Write the first equation as f(x) = 1/2 x2 and the second as g(x) = -1/2 x2 - 8 Suppose that P is a point on the graph of the first equation with first coordinate a. Write the equation of the tangent line to this graph at P. I got y = ax - 1/2 a2 Now suppose that Q is a point on the graph of the second equation with first coordinate b. Write the equation of the tangent line to this graph at Q. I got y = -bx -8 + 1/2 b2 If these two equations give the same line then the slopes are the same a = -b and the y-intersepts are the same - 1/2 a2 = -8 + 1/2 b2 Solve for a and b. Each pair (a,b) that you find gives you a pair of points P and Q. To check you can write the equations of the tangent lines at P and Q to verify they are identical. Cheers, Harley Go to Math Central