how??
Find the condition so that the line px + qy = r intersects the ellipse
x2/a2 + y2/b2 =1 in points whose eccentric anles differ by π / 4
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3 Answers
Lokesh Verma
·2009-03-15 09:07:06
take the point be
(acosθ, b sinθ)
pacosθ + qbsinθ = r
qbsinθ = r-pacosθ
q2b2sin2θ = r2+p2a2cos2θ-2par cosθ
q2b2(1-cos2θ) = r2+p2a2cos2θ-2par cosθ
cos2θ(p2a2+q2b2) - 2parCosθ +r2-q2b2