Question

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

Answer 1

`(x^2)/(4)-(y^2)/(25) =1`

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

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2) =1`

now, we can plug values

`((x-0)^2)/(2^2)-((y-0)^2)/(5^2) =1`

we can simplify it

and we get equation of hyperbola as

`(x^2)/(4)-(y^2)/(25) =1`