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NDA2016MathematicsHyperbolaActual

What is the equation of the hyperbola having latus rectum and eccentrieity 8 and 3 5 respectively?

Options

  1. Ax^2 25 - y^2 20 =1
  2. Bx^2 40 - y^2 20 =1
  3. Cx^2 40 - y^2 30 =1
  4. Dx^2 30 - y^2 25 =1

Correct answer

A. x^2 25 - y^2 20 =1

Step-by-step solution

Let the equation of hyperbola be x^2 a^2 - y^2 b^2 =1 Latus rectum =8= 2 b^2 a ~b ^2=4 a ...(i) aligned & Also, b ^2= a ^2 ( e ^2-1 ) & 4 a = a ^2 ( e ^2-1 ) & 4 a = a ^2 [ ( 3 5 )^2-1 ] & a =5 & ~b ^2=20 & Equation is x^2 25 - y^2 20 =1 aligned [From(i)]

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