Q63 / 125 · BITSAT 2018 · Mathematics

If e1 and e2 are the eccentricities of a hyperbola 3x2-3y2=25 and its conjugate, then

  • A
    e12+e22=2
  • Correct answer
    B
    e12+e22=4
  • C
    e1+e2=4
  • D
    e1+e2=2

Solution

Given equation can be written as

x2-y2=253

∴ e1=1+b2a2

=1+1=2

The equation of conjugate hyperbola is

-x2+y2=253

∴ e2=1+b2a2=1+1=2

∴ e12+e22=22+22=4

Hence, e12+e22=4.

Hence, the correct answer is option: 'B'.

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