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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-8

  • question_answer
    The slope of the normal at the point \[\left( \mathbf{a}{{\mathbf{t}}^{\mathbf{2}}},\mathbf{2at} \right)\] of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\] is

    A)  \[\frac{1}{t}\]                          

    B)  t               

    C)  \[-t\]                            

    D)  \[{{t}^{2}}\]

    Correct Answer: C

    Solution :

                [c] \[\because \]Tangent of the paralbola \[{{y}^{2}}\] \[=4ax\,be\,y.{{y}_{1}}=2a(x+{{x}_{1}})\] At\[\left( a{{t}^{2}},2at \right)\], tangent be \[y.2at=2a\left( x+a{{t}^{2}} \right)\] \[yt=\left( x+a{{t}^{2}} \right)\] \[y=\frac{1}{t}\left( x+at \right)\]slope of the tangent \[=\frac{1}{t}\] So, the slope of the Normal \[=-t\] Hence, the option [c] is correct.


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