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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