vertices (-6,-2) and (0,-2); foci 12 units apart

Question

Find an equation the hyperbola satisfies

Answer 1

Hi Brady!

Be sure to plot what you are given to

better understand what you have.

Vertices are at (-6,-2) and (0,-2), so we

know the transverse axis is horizontal.

(The transverse axis connects the vertices).

The center is halfway between the vertices,

so (h,k) is (-3,-2). And, the distance between

the center and a vertex is a, so a=3.

We are given the foci is 12 units apart. And,

since the distance between foci is also 2c,

2c = 12

--- --- (divide both sides by 2)

2 2

c = 6

Now, all we need is b² to write the equation.

Can use the formula b² = c² - a²

b² = 6² - 3²

b² = 36 - 9

b² = 27

The standard form of a hyperbola with horizontal

transverse axis is:

(x - h)² (y - k)²

-------- - -------- = 1

a² b²

We have h,k,a and b²

Can you use this information

to write the equation?