If the distance between the centres of the hyperbolas :
x 2 – 16xy – 11y 2 – 12x + 6y + 21 = 0 ..... (i)
9x 2 – 16y 2 – 18x – 32y – 151 = 0 ..... (ii) is d then 125 d 2 = .................
Text Solution
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(25)
Sol. Let f (x, y) = x 2 – 16 xy – 11y 2 – 12 x + 6 y + 21
& g (x, y) = 9x 2 – 16 y 2 – 18x – 32 y –151
= 0 ⇒ 2 x – 16y – 12 = 0 ...... (i)
= 0 ⇒ – 16x – 22y + 6 = 0 .......(ii)
Solving (i) & (ii) we get C 1 
Where C 1 is the centre of 1 st hyperbola
Similarly C 2 = (1, – 1)
given that C 1 C 2 = d ⇒ 
+ 
= d 2 = 
∴ 125 d 2 = 25
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