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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    A tangent to the parabola \[{{y}^{2}}=8x\] makes an angle of \[{{45}^{o}}\]with the straight line \[y=3x+5\], then the equation of tangent is

    A)            \[2x+y-1=0\]                             

    B)            \[x+2y-1=0\]

    C)            \[2x+y+1=0\]                             

    D)            None of these

    Correct Answer: C

    Solution :

               \[{{m}_{1}}=\tan 45{}^\circ =1,\] \[{{m}_{2}}=3\]            Slope of tangent \[=\frac{3\pm 1}{1\mp 3}=-2\]or \[\frac{1}{2}\]                    Tangent is \[y=-2x+\frac{2}{-2}\]or \[2x+y+1=0\].


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