Question

Find the equation of hyperbola whose vertices are (±2,0) and the foci are (±3,0)

Answer 1

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

Vertices of hyperbola are form (±a , 0)

Hence,

It is a horizontal ellipse

Now,

Assume

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

Vertices = (±a , 0)

But,

Vertices = (±2 , 0) [Given]

Therefore,

a = 2

Assume,

Foci = (±c , 0)

Foci = (±3 , 0) [Given]

Therefore,

c = 3

b² = (c² - a²)

= (3² - 2²)

= (9 - 4)

= 5

Thus,

a² = 2² = 4

b² = 5

Hence,

$\Large{\boxed{\sf\:{Equation=\dfrac{x^2}{4}-\dfrac{y^2}{5}=1}}}$