Parabolas \[y^2=4a(x-c)\] and \[x^2=4a(y-c')\] where c and c' are variables and touch each other. Locus of their point of contact is :- \[a)xy=a^2\] \[b)xy=2a^2\] \[c)xy=4a^2\] d) None of these

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## Comments

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TopNewestSlope of tangent at point of contact should be same for both the curves.Hence for both the curves take derivative of y with respect to x, substitute the point of contact in the expression obtained by the differentiation and equate.You will then get the required locus as xy=4* (square of a)

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You can find y in terms of x, a, andc' from eqn.2 . Now substitute it in the first eqn to get the soln...

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can you clarify something please:

if \(c\) and \(c'\) are variables, wouldn't the locus correspond to a 3 variable equation?

otherwise, considering them as constants, i get \(c\) as answer

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