Question

The mid point of the chord $4x-3y=5$ of the hyperbola $2x^2-3y^2=12$ is

• A. $(2,1)$
• B. $(0,-\frac{5}{3})$
• C. $(\frac{5}{4},0)$
• D. $(\frac{11}{4},2)$

Answer 1

The correct option is A $(2,1)$

Let mid- point of chord of the hyperbola $\frac{x^2}{6}-\frac{y^2}{4}=1$ is $(x_1,y_1)$. Therefore, the equation of chord is

$\Rightarrow \frac{x{x}_1}{6}-\frac{y{y}_1}{4}-1=\frac{x_1^2}{6}-\frac{y_1^2}{4}-1$

$\Rightarrow \frac{x_1}{6}x-\frac{y_1}{4}y=\frac{x_1^2}{6}-\frac{y_1^2}{4}$

Comparing it with $4x-3y=5$, we get

$x_1=2,y_1=1$