The equation of the chord of contacts of tangents drawn from a point $(2, - 1)$ to the hyperbola $16 x^{2} - 9 y^{2} = 144$ is

9 x + 32 y = 144

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32 x - 9 y = 144

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32 x + 9 y = 144

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none of these

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Solution

The correct option is B $32 x + 9 y = 144$
The equation of the chord of contacts of tangents drawn from $(2, - 1)$ to the hyperbola $16 x^{2} - 9 y^{2} = 144$ is given by
$T = 0$
$\Rightarrow 16 x (2) - 9 y (- 1) = 144 \Rightarrow 32 x + 9 y = 144$
Hence, option 'C' is correct.

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Similar questions

(2, - 1)

16 x^{2} - 9 y^{2} = 144

32 x + 9 y = 144

(x_{1}, y_{1})

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

S S_{1} = T^{2}

S = \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} - 1, S_{1} = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1

T = \frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} - 1

e and $e^{1}$ are the eccentricities of the hyperbolas $16 x^{2} - 9 y^{2} = 144$ and $9 x^{2} - 16 y^{2}$ = - 144 then e - $e^{1}$ =

16 x^{2} + 9 y^{2} = 144

16 x^{2} - 9 y^{2} = - 144

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