JEE Main & Advanced Sample Paper JEE Main Sample Paper-45

  • question_answer
    Direction: A straight line will touch a given conic if there is only one point of intersection of the line and the given conic. If the conic is specified by quadratic equation in\[x\] and \[y,\] then the straight line will touch if the discriminant of the equation obtained by the elimination of one of the variable is zero. Let us consider parabola \[{{y}^{2}}=8x\] and an ellipse\[15{{x}^{2}}+4{{y}^{2}}=60\].
    The equation of the normal at the point of contact of the common tangent which makes an acute angle with the positive direction of \[x-\]axis to the parabola is

    A)  \[2x+y-24=0\]          

    B)  \[2x+y-48=0\]

    C)  \[2x+y+48=0\]        

    D)  \[2x+y+24=0\]

    Correct Answer: A

    Solution :

     Equation of tangent is \[x-2y+8=0\]              ?(i) Let the point of contact is \[({{x}_{1}},\,{{y}_{1}})\] then the equation of tangent to the curve \[{{y}^{2}}=8x\] is \[y{{y}_{1}}-4x-4{{x}_{1}}=0\]     ?(ii) On comparing Eqs. (i) and (ii), we get \[\frac{1}{-4}=\frac{-2}{{{y}_{1}}}=\frac{8}{-4{{x}_{1}}}\] \[\Rightarrow \]            \[2x+y-24=0\]

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