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Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseChord of ContactHard3 minQB

MathematicsHardsingle choice

The ellipse $x^{2} + 4 y^{2} = 4$ is cut by $x^{2} + 4 y^{2} + λ x y = 0$ at $A, B$ . Find the locus of the intersection of tangents at $A, B$ .

Options:

Answer:

Solution:

If the tangent intersection is $(h, k)$ , its chord of contact is $x h /4 + y k = 1$ . Comparing the induced pair of lines gives $h^{2} - 4 k^{2} = 0$ .

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:Chord of Contact

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