How do you 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?

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Answer 1 · 2017-04-17T05:40:26

The process in described in the explanation.

Here is the equation of a hyperbola with a vertical transverse axis:

#(y - k)^2/a^2-(x-h)^2/b^2=1" [1]"#

We are given that the center is the origin; this means that #h=k=0#

#(y - 0)^2/a^2-(x-0)^2/b^2=1" [2]"#

We are given that #a = 12#:

#(y - 0)^2/12^2-(x-0)^2/b^2=1" [2]"#

We are given that the foci are 26 inches apart; this means that the focal length is 13:

#13 = sqrt(a^2+b^2)#

#13^2 = 12^2+b^2#

#b = sqrt(169-144)#

#b = sqrt(25)#

#b = 5#

#(y - 0)^2/12^2-(x-0)^2/5^2=1 larr# answer