If x = 9 is the chord of contact of the hyper | vedclass

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(B) The equation of the chord of contact for a point $(h, k)$ with respect to the hyperbola $S: x^2 - y^2 - 9 = 0$ is given by $T = 0$,which is $xh -

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

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(B) The equation of the chord of contact for a point $(h, k)$ with respect to the hyperbola $S: x^2 - y^2 - 9 = 0$ is given by $T = 0$,which is $xh - yk - 9 = 0$.Comparing this with the given chord $x = 9$ (or $x - 9 = 0$),we get $h = 1$ and $k = 0$.The equation of the pair of tangents from a point $(h, k)$ to the hyperbola is given by $SS_1 = T^2$.Here,$S = x^2 - y^2 - 9$,$S_1 = (1)^2 - (0)^2 - 9 = 1 - 9 = -8$,and $T = x(1) - y(0) - 9 = x - 9$.Substituting these into the formula: $(x^2 - y^2 - 9)(-8) = (x - 9)^2$.$-8x^2 + 8y^2 + 72 = x^2 - 18x + 81$.Rearranging the terms: $9x^2 - 8y^2 - 18x + 9 = 0$.

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

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