One approach would be to get the equation of the tangent at P. You can do this the same way as your hyperbola question: http://www.mathhelpforum.com/math-he...a-problem.html.

Substitute x = -a into the equation of the tangent to get the y-coord of Q and hence distance AQ.

Substitute x = a into the equation of the tangent to get the y-coord of R and hence distance BR.

Now calculate dAQ.dBR and hope you get b^2 as the answer.