Question

The equation of the chord of the hyperbola $25x^2-16y^2=400$ that is bisected at point $(5,3)$ is:

• A. $135x-48y=481$
• B. $125x-48y=481$
• C. $125x-4y=48$
• D. None of these

Answer 1

Answer: (B)

The equation of the chord, having mid-point as $(x_1,y_1)$, of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is given by
$T=S_1...\left(i\right)$
where, $T=\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}-1$ and
$S_1=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1$
According to the question,
$\left(x_1,y_1\right)=\left(5,3\right)$ and $a^2=16,b^2=25$
as $25x^2-16y^2=400$
$\Rightarrow \frac{x^2}{16}-\frac{y^2}{25}=1\therefore \frac{5x}{16}-\frac{3y}{25}=\frac{25}{16}-\frac{9}{25}\left[Using\left(i\right)\right]$
$\Rightarrow 125x-48y=625-144\Rightarrow 125x-48y=481$