For different values of k and l the two parabolas y 2 = 16 ( x − k ) , x 2 = 16 ( y − l ) always touch each other then locus of point of contact is

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y 2 = 16 ( x − k ) x 2 = 16 ( y − l ) 2 y d x d y ​ = 16 ​ 2 x = 16 d x d y ​ d x d y ​ = y 8 ​ = m 1 ​ ​ d x d y ​ = 8 x ​ = m 2 ​ ​ Since two circle touch each other m 1 ​ = m 2 ​ ⇒ y 8 ​ = 8 x ​ ⇒ x y = 64

Mathematics - Parabola Question with Solution | TestHub

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