Question

A hyperbola has a center at the origin, a vertex at (9, 0), and a focus at (41, 0). What is the equation of the hyperbola?

Answer 1

Answer:

a on edge

Step-by-step explanation:

just bc it is

Answer 2

The equation of hyperbola is

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

Where center is (h,k)

Vertex is(h+a,k)

SO if we compare the vertex with the vertex formula, we will get

$h+a=9, k=0$

And formula of focus is (h+c,k)

On comparing we will get

$h+c=41$

So we have h =0 , k=0, a=9, c=41

$b^2=c^2-a^2\\b^2=41^2-9^2\\b^2=1600$

So the equation is

$\frac{x^2}{81}-\frac{y^2}{1600}=1$