Question

Find the equation to the chord of contact of tangents drawn from a point p(4, 3) to the hyperbola

$\frac{x^2}{16}-\frac{y^2}{9}=1$

• A. 4x + 3y = 12
• B. 3x - 4y = 12
• C. 3x + 4y = 12
• D. 4x - 3y = 12

Answer 1

The correct option is B

3x - 4y = 12

Equation to the chord of contact of tangents drawn from a point $p(x_1,y_1)$ to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ is

T=0

$\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}-1=0$

Here ,point is (4, 3) to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

Equation of chord of contact is T=0

$\frac{4x}{16}-\frac{3y}{9}-1=0$

$\frac{x}{4}-\frac{y}{3}-1=0$

3x-4y=12