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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    The two parabolas \[{{x}^{2}}=4y\]and \[{{y}^{2}}=4x\]meet in two distinct points. One of these is the origin and the other is

    A) \[(2,2)\]                              

    B)        \[(4,-4)\]                             

    C)        \[(4,4)\]                              

    D)                        \[(-2,2)\]

    Correct Answer: C

    Solution :

    Given, equations of parabola are \[{{x}^{2}}=4y\]and \[{{y}^{2}}=4x\]                                                ?(i)                 \[\therefore \]  \[{{\left( \frac{{{x}^{2}}}{4} \right)}^{2}}=4x\Rightarrow {{x}^{4}}-64x=0\] \[\Rightarrow \]               \[x=0,x=4\] On putting the value of x in Eq. (i), we get \[y=0\]and \[y=4,-4\] (\[\because \,\,y=-4\]does not satisfy the equation\[{{x}^{2}}=4y\]) Hence, points of intersection are (0, 0) and (4, 4).


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