Question

In each of the following find the equations of the hyperbola satisfying the given conditions foci (±5, 0), transverse axis = 8

Answer 1

To find: equation of the hyperbola 

Formula used: 

The standard form of the equation of the hyperbola is,

Length of transverse axis is 2a 

Coordinates of the foci for a standard hyperbola is given by (±ae, 0) 

According to question:

2a = 8 and ae = 5 

2a = 8

We know, 

b² = a²(e² – 1)

⇒ b² = 4(21) 

⇒ b² = 84 

Hence, the equation of the hyperbola is: