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If \mathrm{x=8} is the chord of contact of the hyperbola \mathrm{}\mathrm{}\mathrm{x^2-y^2=8 } then the equation of the corresponding pair of tangents is

Option: 1

8 x^2-7 y^2+16 x-8=0


Option: 2

8 x^2-7 y^2+16 x+8=0


Option: 3

8 x^2-7 y^2-16 x-8=0


Option: 4

8 x^2-7 y^2-16 x+8=0


Answers (1)

best_answer

Let P\left(x_1, y_1\right) be a point from which the tangents are

drawn to the hyperbola x^2-y^2=8

The equation of chord of contact of P\left(x_1, y_1\right) is T=0 \, \, x x_1-y y_1-8=0

and x=8 is also the equation of

chord of contact of P.

Then x_1=1, y_1=0

\therefore \quad P(1,0)

Equation to the pair of tangents from P(1,0) is T^2=S S_1\, \, i.e., (x-8)^2=-7\left(x^2-y^2-8\right)

or 8 x^2-7 y^2-16 x+8=0.

Posted by

Divya Prakash Singh

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