Question

The equation of the hyperbola with center at (0, 0) opening horizontally, with a = 2, b = 5 is:

Answer 1

Answer:

$\frac{x^2}{4}-\frac{y^2}{25} =1$

Step-by-step explanation:

we are given

center =(0,0)

we can compare with

center=(h,k)=(0,0)

so, h=0 and k=0

a=2 and b=5

now, we can use equation of hyperbola formula

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1$

now, we can plug values

$\frac{(x-0)^2}{2^2}-\frac{(y-0)^2}{5^2} =1$

we can simplify it

and we get equation of hyperbola as

$\frac{x^2}{4}-\frac{y^2}{25} =1$