Question

The mid-point of the chord intercepted by the hyperbola $9x^2-16y^2=144$ on the line $9x-8y-10=0$, is:

• A. $(1,2)$
• B. $(-1,2)$
• C. $(-2,1)$
• D. $(2,1)$

Answer 1

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

Let mid point of the chord is $P(h,k)$
Thus its equation is given by,
$\frac{hx}{16}-\frac{ky}{9}=\frac{h^2}{16}-\frac{k^2}{9}..\left(1\right)$
Comparing it with given equation,
$\frac{h}{16\times 9}=\frac{k}{9\times 8}=\frac{\frac{h^2}{16}-\frac{k^2}{9}}{10}$
Solving this equation we get $h=2,k=1$
Hence required point is $(2,1)$