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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

  • question_answer
    The equation of tangent to the parabola \[{{y}^{2}}=8x\]which is perpendicular to the line \[2x-y+1=0,\]is

    A)  \[x+2y=8\]       

    B)  \[x+2y+8=0\]

    C)  \[2x+y=8\]       

    D)  \[2x+y+8=0\]

    Correct Answer: B

    Solution :

     Given, line is\[2x-y+1=0\]\[\Rightarrow \]\[y=2x+1\] and      parabola \[{{y}^{2}}=8x\] \[\Rightarrow \] \[a=2\] Slope of line = 2 Slope of perpendicular line \[=-\frac{1}{2}=m\] Condition of tangency is \[c=\frac{a}{m}\] \[\Rightarrow \] \[c=\frac{2}{-1/2}=-4\] Hence, equation of tangent is\[y=-\frac{1}{2}x-4\] \[\Rightarrow \] \[2y=-x-8\] \[\Rightarrow \] \[x+2y+8=0\]


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