Question

The equation of the chord of contact of tangents drawn from a point (2, –1) to the hyperbola$2x^{2} + 5xy + 2y^{2} + 4x + 5y + 2 = 0$ is

• A. $32x + 9y = 144$
• B. $32x + 9y = 55$
• C. $32x + 9y + 144 = 0$
• D. $32x + 9y + 55 = 0$

Answer 1

Answer: (A)

$32x + 9y = 144$

Answer 2

From $T = 0$ i.e., $\frac{xx_{1}}{a^{2}} - \frac{yy_{1}}{b^{2}} = 1$. Here, $16x^{2} - 9y^{2} = 144$ i.e., $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$

So, the equation of chord of contact of tangents drawn from a point (2, –) to the hyperbola is $\frac{2x}{9} - \frac{( - 1)y}{16} = 1$

i.e., $32x + 9y = 144$