Question

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

• A. 115x - 117y = 17
• B. 125x - 48y = 481
• C. 127 + 33y = 341
• D. 15x + 121y = 105

Answer 1

The correct option is B

125x - 48y = 481

Equation of the chord whose middle point is given

$T=s_1$

According to the question $s_1=25x_1^2-16y_1^2-400=0$

$(x_1,y_1)\equiv (5,3)$

$S_1=25\times (5{)}^2-16(3{)}^2-400$

$=625-144-400=81$

and $T=25x{x}_1-16y{y}_1-400$

$T=25x\left(5\right)-16y\left(3\right)-400$

$T=125x-48y-400$

so,the equation of the required chord is

$125x-48y-400=81$

or

$125x-48y=481$