let the pt of intersection be (acosθ,bsinθ) and (acos(θ+pi/4),bcos(θ+pi/4))
these two points lie on the line px+qy=r eliminate theta and then u will get the reqd condion.
Find the condition such that the line px+qy=r
intersects ellipse x2/a2 + y2/b2 =1
in points whose eccentric angles differ by π/4
Hint: the line is equation of chord of contact of the two tangents at the points mentioned
let the pt of intersection be (acosθ,bsinθ) and (acos(θ+pi/4),bcos(θ+pi/4))
these two points lie on the line px+qy=r eliminate theta and then u will get the reqd condion.