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Question

If e1 and e2 are the eccentricities of a hyperbola and its conjugate respectively, Then e21+e22=1.
  1. False

  2. True


Solution

The correct option is B

True


We have to remember the relation between the eccentricities of both the hyperbolas with their respectives axes lengths.

Here,

e21=1+b2a=a2+b2a2

And corresponding parameter for its conjugate hyperbola can be obtained by interchanging the position of  a and b. ife2 is the eccentricity of the conjugate hyperbola,Then,

e22=1+a2b2=a2+b2a2

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