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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    TP and TQ are tangents drawn to parabola \[{{y}^{2}}=4x\] at \[P({{x}_{1}},{{y}_{1}})\]and \[Q({{x}_{2}},{{y}_{2}})\] where \[{{y}_{1}}{{y}_{2}}>0\]. If \[\frac{{{x}_{1}}}{{{x}_{2}}}=16,\] then the locus of point T is

    A) \[4{{y}^{2}}=25x\]   

    B)        \[2{{y}^{2}}=25x\]          

    C)   \[3{{y}^{2}}=16x\]          

    D)        \[3{{y}^{2}}=20\]

    Correct Answer: A

    Solution :

    [a] Let \[P(a{{t}_{1}}^{2},2a{{t}_{1}}),\,\,Q(a{{t}_{2}}^{2},2a{{t}_{2}})\] and \[T(h,k)\] Here,  \[h={{t}_{1}}{{t}_{2}},\,\,\,k={{t}_{1}}+{{t}_{2}}.\] Also,  \[{{t}_{1}}^{2}=16{{t}_{2}}^{2}\] (given) Eliminating \[{{t}_{1}}\] and \[{{t}_{2}},\] we get locus of \[T(h,k)\] as \[4{{y}^{2}}=25x.\]


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