Verified Solution • 2025–26 Session moderate

QJEEM19Ma3596: JEE Main 2019 Mathematics - Class 11 JEEM19Ma3596 Solution: A hyperbola has its centre at the origin, passes through the…

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

Multiple Choice Options

  • A 32
  • B 3
  • C 2
  • D 23

Step-by-Step Verified Solution

Let the equation of hyperbola

x2a2−y2b2 = 1

Given 2a = 4

⇒  a = 2

It passes through (4, 2)

∴  164−4b2 = 1

⇒  b2 = 43

e = 1+b2a2 = 1+4/34

= 1+13 = 23

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