A line intersencts hte ellipse x2/a2 +y2/b2=1 at P and Q and the parabola y2=4d(x+a) at R and S.The line segment PQ subtend right angle at the centre of ellipse.Find the locus of hte point of intersection of tangents
to the parabola at R and S
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1 Answers
11let 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.
