Find an equation that models a hyperbolic lens with a = 12 inches and foci that are 26 inches apart. Assume that the center of the hyperbola is the origin and the transverse axis is vertical.

The general form for a hyperbola with the center at the origin and a vertical transverse axis is:

y2/a2 - x2/b2 = 1

From the given:

a = 12

To get b, we use the given distance between the foci. Since it's 26,

c = 26/2 = 13

Using this defintion:

c2 = a2 + b2

b = sqrt (c2 - a2) = sqrt (13^2 - 12^2) = 5

The equation therefore is:

y2/13^2 - x2/5^2 = 1

or

y2/169 - x2/25 = 1