ellipse..dbt

let one point where the line intersects the ellipse be (acosθ , asinθ) .
Therefore the other points is (acos(θ+90) , asin(θ+90) ) .

Now the eq of the chord is x/acos(θ+45) = - y/bsin(θ+45) .

solve this with the eq of the parabola to find the 2 points of intersection.

the points obtained may be rearranged to the form (at²,2at) so that the points of intersection may be obtained as (at₂at₃ , 2a(t₂+t₃)) .

now h=at₂at₃ , k=2a(t₂+t₃). you t₂ and t₃ in terms of θ . eliminate θ.