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10-2. Parabola, Ellipse, Hyperbola
hard
What will be equation of that chord of hyperbola $25{x^2} - 16{y^2} = 400$, whose mid point is $(5, 3)$
A
$115x - 117y = 17$
B
$125x - 48y = 481$
C
$127x + 33y = 341$
D
$15x + 121y = 105$
Solution
(b) According to question, $S \equiv \,25{x^2} – 16{y^2} – 400 = 0$
Equation of required chord is ${S_1} = T$…..$(i)$
Here, ${S_1} = 25{(5)^2} – 16{(3)^2} – 400$
$ = 625 – 144 – 400 = 81$
and $T \equiv 25x{x_1} – 16y{y_1} – 400,$
where ${x_1} = 5,\,{y_1} = 3$
$ = 25(x)(5) – 16(y)(3) – 400$$ = 125x – 48y – 400$
So from $(i),$ required chord is
$125x – 48y – 400 = 81$ or $125x – 48y = 481.$
Standard 11
Mathematics
