JEE Main & Advanced JEE Main Paper (Held On 12 April 2014)

  • question_answer
    Two tangents are drawn from a point (- 2, - 1) to the curve, \[{{y}^{2}}=4x.\] If \[\alpha \] is the angle between them, then \[|\tan \alpha |\]is equal to:   [JEE Main Online Paper ( Held On 12 Apirl  2014 )

    A) \[\frac{1}{3}\]                                   

    B) \[\frac{1}{\sqrt{3}}\]

    C) \[\sqrt{3}\]                                        

    D) \[3\]

    Correct Answer: D

    Solution :

    The locus of the point of intersection of tangents to the parabola \[{{y}^{2}}=4ax\] inclined at an angle \[\alpha \] to each other is\[{{\tan }^{2}}\alpha {{(x+a)}^{2}}={{y}^{2}}-4ax\] Given equation of Parabola \[{{y}^{2}}=4x\{a=1\}\] Point of intersection (-2, -1) \[{{\tan }^{2}}\alpha {{(-2+1)}^{2}}={{(-1)}^{2}}-4\times 1\times (-2)\] \[\Rightarrow \]\[{{\tan }^{2}}\alpha =9\]\[\Rightarrow \]\[\tan \alpha =\pm 3\]\[\Rightarrow \]\[|\tan \alpha |=3\]

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