Question

Find the equation of hyperbola whose foci are (±5,0) and the transverse axis is of length 8

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the:Question}}}}$

Foci of hyperbola are form (±a , 0)

Hence,

It is a horizontal ellipse

Now,

Assume

${\boxed{\sf\:{Equation=\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}}}$

Length of transverse axis = 2a

Therefore,

2a = 8

a = 4

a² = 16

Assume,

Foci = (±c , 0)

Then,

c = 5

Therefore,

Foci = (±5 , 0)

b² = (c² - a²)

= (5² - 4²)

= (25 - 16)

= 9

a² = 16

b² = 9

Hence,

$\Large{\boxed{\sf\:{Equation=\dfrac{x^2}{16}-\dfrac{y^2}{9}=1}}}$