C Secure https O CONC SECTIONS Writing an equation of a hype

>C Secure https: O CONC SECTIONS -Writing an equation of a hyperbola given the foci and the vertices Find an equation of the hyperbola having foci at (o, 5) and (12, 5) and vertices at (3, 5) and (9, 5) Check

Solution

foci ( 0,5 ) and (12, 5 )

vertices ( 3,5 ) and (9, 5 )

h + a = 3

h - a = 9

2h = 12

h = 6

k = 5

hence, center = ( 6 , 5 )

a^2 = 9

b^2 = 36 - 9

b^2 = 27

hence , the equation of hyperbola is

( x - 6)^2 / 9 - ( y - 5)^2 / 27 = 1