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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2005

  • question_answer
    The equation of the normal to the parabola \[{{y}^{2}}=4x\]which is parallel to the line \[y=2x-5,\]is

    A)  \[y=2x\]           

    B)  \[y=2x-10\]

    C)  \[y=2x+10\]      

    D)  \[y=2x-12\]

    Correct Answer: D

    Solution :

     Given, equation of parabola is \[{{y}^{2}}=4x.\] Here        \[a=1\] Equation of line is \[y=2x-5.\] Slope \[m=2\] Since, normal is parallel to line. \[\therefore \]Slope of normal\[=2\] \[\therefore \]Equation of normal is \[y=mx-2am-{{m}^{3}}\] \[\Rightarrow \] \[y=2x-2.1.2-{{(2)}^{3}}\] \[\Rightarrow \] \[y=2x-4-8\] \[\Rightarrow \] \[y=2x-12\]


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