Find the standard form of the equation of the hyperbola with the given characteristics?

Question

Vertices: (-2, 1) and (2, 1)

Foci: (-3, 1) and (3, 1)

Answer 1

The equation has the form (horizontal hyperbola)

(x-h)/a²-(y-k)²/b²=1.

Now we have to 

1. Identify the center point (h, k)
2. Identify a and b, where  c²=a²+b²

The center point is (0, 1). To find a, we'll count from the center to either vertex; a=2. To find c, we'll count from the center to either focus. c=3
We'll use the formula c²=a²+b² to find b. To do that, we'll sub in a=2 and c=2, then solve for b; b²=9-4=5.

 

Now we have h=0, k=3, a=2, b=√5.

The equation is x²/4-(y-3)²/5=1.