• # 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)            $9{{x}^{2}}-8{{y}^{2}}+18x+9=0$

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$9{{x}^{2}}-8{{y}^{2}}-18x+9=0$.