Question

The equation of the chord of hyperbola $25x^2-16y^2=400$ whose mid point is $(5,3)$

• A. $115x-47y=434$
• B. $125x-48y=481$
• C. $127x-49y=488$
• D. $155x-67y=574$

Answer 1

Answer: (B)

$125x-48y=481$

Equation of hyperbola is $25x^2-16y^2=400$

Therefore, $\frac{x^2}{16}-\frac{y^2}{25}=1$

Equation of chord with mid point $(5,3)$ is $T=S^{\prime }$.

$\Rightarrow \frac{x{x}_1}{16}-\frac{y{x}_1}{25}=\frac{x_1^2}{16}-\frac{y_1^2}{25}\Rightarrow \frac{5x}{16}-\frac{3y}{25}=\frac{5^2}{16}-\frac{3^2}{25}\Rightarrow \frac{125x-48y}{16\left(25\right)}=\frac{625-144}{16\left(25\right)}\Rightarrow 125x-48y=481$

So, option B is correct.