Question

Find the equation to the chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(5,3)$.

Answer 1

Let the equation of chord be $(y-y_1)=m(x-x_1)$ for the hyperbola $\frac{x^2}{16}-\frac{y^2}{25}=1$

Differentiating w.r.t $x$ we get

$\frac{dy}{dx}=\frac{25x}{16y}$

At point $(5,3)$

$m=$$\frac{25\times 5}{16\times 3}$

Putting $m$ in the equation of chord, we get

$(y-5)=$$\frac{25\times 5}{16\times 3}$$(x-3)$

So, the equation of chord is

$125x-48y=481$