11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer The point of intersection of the tangents at the ends of the latus rectum of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4x}\] is

    A) \[\left( 1,0 \right)\]                      

    B) \[\left( 0,1 \right)\]          

    C) \[\left( 0,-1 \right)\]                     

    D) \[\left( -1,0 \right)\]

    Correct Answer: D

    Solution :

    [d] The coordinate of extremities of the latus rectum of \[{{y}^{2}}=4x\] be (1, 2) and\[\left( 1,-2 \right)\]. So, the equation of the tangents at (1, 2) and \[\left( 1,-2 \right)\] be \[2y=\frac{4\left( x+ \right)}{2}\Rightarrow y=x+1\]                  ??...(1) \[-2y=\frac{4\left( x+ \right)}{2}\Rightarrow -y=x+1\]             ?.......(2) Solving equation (1) and (2), we have \[2\left( x+1 \right)=0\] \[x=-1\]and \[y=0\] Thus, required point be (? 1, 0). Hence, option [d] is correct


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