Conic Sections Question 393
Question: What will be equation of that chord of hyperbola $ 25x^{2}-16y^{2}=400 $ , whose mid point is (5, 3)
[UPSEAT 1999]
Options:
A) $ 115x-117y=17 $
B) $ 125x-48y=481 $
C) $ 127x+33y=341 $
D) $ 15x+121y=105 $
Show Answer
Answer:
Correct Answer: B
Solution:
According to question, $ S\equiv 25x^{2}-16y^{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 25xx_1-16yy_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. $
BETA
