How to 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?

Question

Anya Rice · Accepted Answer

The hyperbola&#039;s equation with a vertical transverse axis is as follows:                              (          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    =                            a          2                +                  b          2                                13      2        =          12      2        +          b      2            b    =                  169        -        144                  b    =                  25                  b    =    5                                (          y          -          0          )                2                    12        2              -                            (          x          -          0          )                2                    5        2              =    1    ←   answer

How to 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?

Answered question

Answer & Explanation

New Questions in High school geometry