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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    If curves \[~{{x}^{2}}=9a(9-y)\]and \[~{{x}^{2}}=a\text{ (y + 1)}\]intersect orthogonally then value of 'a' is

    A)  1                                            

    B) (2) 2

    C)  3                                            

    D)  4

    Correct Answer: D

    Solution :

    For\[{{x}^{2}}=9a(9-y);\]\[\frac{dy}{dx}=\frac{-2x}{9a}={{m}_{1}}\] For\[{{x}^{2}}=a(y+1);\]\[\frac{dy}{dx}=\frac{2x}{a}={{m}_{2}}\] \[{{m}_{1}}{{m}_{2}}=-1\]gives\[4{{x}^{2}}=9{{a}^{2}}\]                ?(1) also by eliminating ?y? between the equation of curves \[{{x}^{2}}=9a\]                                 ?(2) from (1) and (2), we get a = 4


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