Find an equation that models a hyperbolic lens with a = 16 inches and foci that are 40 inches apart. assume that the center of the hyperbola is the origin and the transverse axis is vertical.

The answer is:


Explanation:
The general equation for a hyperbola with transverse axis vertical is

where:
h = x-coordinate of the center
k = y-coordinate of the center
a = semi-major axis
b = semi-minor axis

We know that the center has coordinates (0, 0), therefore:
h = 0
k = 0

We also know that
a = 16
2c = distance between foci = 40

In order to find b², we need to use the formula 
c² = a² + b²

and solve it for b²:
b² = c² - a²
    = (40÷2)² - 16²
    = 400 - 256
    = 144

Now we can substitute the obtained values in the general equation to find the required equation: