This is from Cambridge 4 unit ex 3.2 question 7
P(a cos θ , b sin θ) and Q(a cos ɸ, b sin ɸ) lie on the ellipse x^2/ a^2 + y^2/a^2 = 1
a) In PQ subtends a right angle at (0,0) show that tanθ tanɸ = - a^2/b^2
b) If PQ subtends a right angle at (a,0) show that tanθ/2 tanɸ/2 = - b^2/a^2