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Parabolas y² = 4a(x–k) and x² = 4a(y–l) are such that they touch each other. (k,l are variables ) locus of point of contact is xy = ma² then m =

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answer is 4.

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Detailed Solution

$y^{2} = 4 a (x - k), x^{2} = 4 a (y - l),$

$f o r t h e f i r s t c u r v e \frac{d y}{dx} (m_{1}) = \frac{2 a}{y}, f o r t h e s e c o n d c u r v e \frac{dy}{dx} (m_{2}) = \frac{x}{2 a} c u r v e s t o u c h e a c h o t h e r \Rightarrow m_{1} = m_{2} \frac{2 a}{y} = \frac{x}{2 a} \Rightarrow xy = 4 a^{2}$

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