NDA2016MathematicsHyperbolaActual
What is the equation of the hyperbola having latus rectum and eccentrieity 8 and 3 5 respectively?
Options
- Ax^2 25 - y^2 20 =1
- Bx^2 40 - y^2 20 =1
- Cx^2 40 - y^2 30 =1
- 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)]