11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer If \[x=9\] is the chord of contact of the hyperbola \[{{x}^{2}}-{{y}^{2}}=9\], then the equation of the corresponding pair of tangents is  [IIT 1999]

    A)            \[9{{x}^{2}}-8{{y}^{2}}+18x-9=0\]

    B)            \[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\]    

    C)            \[9{{x}^{2}}-8{{y}^{2}}-18x-9=0\]

    D)            \[9{{x}^{2}}-8{{y}^{2}}+18x+9=0\]

    Correct Answer: B

    Solution :

               The equation of chord of contact at point \[(h,k)\] is \[xh-yk=9\]            Comparing with \[x=9,\] we have \[h=1,\,k=0\]            Hence equation of pair of tangent at point (1,0) is \[S{{S}_{1}}={{T}^{2}}\]            Þ\[({{x}^{2}}-{{y}^{2}}-9)({{1}^{2}}-{{0}^{2}}-9)={{(x-9)}^{2}}\]            Þ\[-8{{x}^{2}}+8{{y}^{2}}+72={{x}^{2}}-18x+81\]                    Þ\[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\].


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