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if e and e1 be the eccentricity of the hyperbola and conjugate hyperbola then e1 ^2 – e^2=???? a)e^2. e1 ^2 – 2e^2 b)e^2. e1 ^2+ 2e^2 c)2e^2- e^2. e1 ^2 d)2e^2 + e1 ^2 please give solution

if e and e1 be the eccentricity of the hyperbola and conjugate hyperbola then e1 ^2 – e^2=????
a)e^2. e1 ^2 – 2e^2
b)e^2. e1 ^2+ 2e^2
c)2e^2- e^2. e1 ^2
d)2e^2 + e1 ^2
please give solution

Grade:12

1 Answers

Arun
25750 Points
4 years ago
 

The eccentricity e1 of the given hyperbola is obtained from

b2 = a2(e12 – 1).                                                  …… (1)

The eccentricity e2 of the conjugate hyperbola is given by

a2 = b2(e22 – 1).                                                  …… (2)

Multiply (1) and (2), we get,

1 = (e12 – 1)(e22 – 1) ⇒ 0 = e12 e22 – e12 – e22

⇒ e1–2 + e2–2 = 1.

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