The line ( x /2 ) cos θ + y sin θ = 1 , with θ ∈ ( π /18 , π /15 ) , cuts x 2 + 2 y 2 = 6 at P , Q . Find the angle between tangents at P , Q .

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MathematicsEllipseTangents & NormalsHard3 minQB

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The line $(x /2) cos θ + y sin θ = 1$ , with $θ \in (π /18, π /15)$ , cuts $x^{2} + 2 y^{2} = 6$ at $P, Q$ . Find the angle between tangents at $P, Q$ .

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Answer:

Solution:

Comparing the chord of contact $h x + 2 k y = 6$ gives $h^{2} + k^{2} = 9$ , the director circle of the ellipse. Thus the tangents are perpendicular.

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:Tangents & Normals

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