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

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

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

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

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

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Solution

The correct option is B $9 x^{2} - 8 y^{2} - 18 x + 9 = 0$
If x = 9 meets the hyperbola at $(9, 6 \sqrt{2})$ and $(9, - 6 \sqrt{2})$ .
Then, equations of tangent at these points are $3 x - 2 \sqrt{2} y - 3 = 0$ and $3 x + 2 \sqrt{2} y - 3 = 0$ .
The combined equation of these two is $9 x^{2} - 8 y^{2} - 18 x + 9 = 0$ .

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