NDA 2023 Maths · Mathematics · Conic Sections · medium

A hyperbola has transverse axis of length 8 and conjugate axis of length 6. Its eccentricity is

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A hyperbola has transverse axis of length

8

and conjugate axis of length

6

. Its eccentricity is

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Answer: (D) $\dfrac54$

Here

2a=8

and

2b=6

, so

a=4

b=3

e=\sqrt{1+b^2/a^2}=\sqrt{1+\tfrac9{16}}=\dfrac54

. The value

\dfrac53

swaps

a

and

b

, and

\dfrac{\sqrt7}{4}

uses

a^2-b^2

, which is the ellipse formula.

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