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docker41 [41]
3 years ago
8

Find an equation that models a hyperbolic lens with a = 12 inches and foci that are 26 inches apart. Assume that the center of t

he hyperbola is the origin and the transverse axis is vertical.
Mathematics
1 answer:
marta [7]3 years ago
8 0
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
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