11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer The equation of a circle passing through the vertex and the extremities of the latus rectum of the parabola \[{{y}^{2}}=8x\] is [MP PET 1998]

    A)            \[{{x}^{2}}+{{y}^{2}}+10x=0\]   

    B)            \[{{x}^{2}}+{{y}^{2}}+10y=0\]

    C)            \[{{x}^{2}}+{{y}^{2}}-10x=0\]    

    D)            \[{{x}^{2}}+{{y}^{2}}-5x=0\]

    Correct Answer: C

    Solution :

               For parabola, \[{{y}^{2}}=8x\]Þ\[4a=8\]Þ\[a=2\]            vertex of \[{{y}^{2}}=8x,\,\,O\equiv (0,0)\]            End points of latus-ractum            \[L(a,2a);\,L'(a,-2a)\] Þ\[L(2,4);L'(2,-4)\]            Circle passes through the point (0,0) (2,4) and (2,?4)            Let equation of circle, \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]            \ After solving equation of circle,\[{{x}^{2}}+{{y}^{2}}-10x=0\]                    Trick: option (c) satisfied by (2, 4) and (2,?4).


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