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Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseTangent to ellipseMedium2 minQB

MathematicsMediumnumerical

A tangent to $x^{2} / a^{2} + y^{2} / b^{2} = 1$ meets the positive axes at $P, Q$ . Point $R$ divides $PQ$ internally in the ratio $2 : 1$ . If the locus of $R = (x, y)$ is $a^{2} / x^{2} + 4 b^{2} / y^{2} = λ$ , find $λ$ .

Answer:

9.00

Solution:

The tangent intercepts are $(a / cos θ, 0), (0, b / sin θ)$ . Thus $R = (a / (3 cos θ), 2 b / (3 sin θ))$ , yielding $a^{2} / x^{2} + 4 b^{2} / y^{2} = 9$ .

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:Tangent to ellipse

⏱ 2mℹ️ Source: QB

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