If a variable tangent of the hyperbola 9 x 2 − 4 y 2 = 1 , cuts the circle x 2 + y 2 = 4 at point A , B and locus of mid point of AB is 9 x 2 − 4 y 2 − λ ( x 2 + y 2 ) 2 = 0 then λ is … .

Equation of chord of circle with mid point ( h , k ) is xh + xk = h 2 + k 2 or y = ( k − h ) x + k h 2 + k 2 , it touches the hyperbola

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Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaTangents & NormalsMedium2 minQB

MathematicsMediuminteger

If a variable tangent of the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ , cuts the circle $x^{2} + y^{2} = 4$ at point $A, B$ and locus of mid point of AB is $9 x^{2} - 4 y^{2} - λ (x^{2} + y^{2})^{2} = 0$ then $λ$ is $\dots$ .

Answer:

Solution:

Equation of chord of circle with mid point $(h, k)$ is $xh + xk = h^{2} + k^{2}$ or

$y = (\frac{- h}{k}) x + \frac{h ^{2} + k ^{2}}{k}$ , it touches the hyperbola

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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