Discussion Forum

The equation of the chord of the hyperbola 25x² - 16y2 = 400, that is bisected at point (5,3) is:

Answer:

Explanation:

The equation of the chord, having mid-point  as (x_1, y₁), of the hyperbola

$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1$ is given by T = S₁ ....(i)

Where, T = $\frac{xx_{1}}{a^{2}}-\frac{yy_{1}}{b^{2}}-1$

and S₁ = $\frac{x_{1}^{2}}{a^{2}}-\frac{y_{1}^{2}}{b^{2}}-1$

According to the question,  (x_1, y₁) = (5, 3) and a² = 16 b² = 25

and 25x² - 16y² = 400,

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

$\frac{5x}{16}-\frac{3y}{25} =\frac{25}{16}-\frac{9}{25}$

                                                             [using (i)]

125x - 48y = 625 - 144 = 125x - 48y = 481