PLEASE PLEASE ANSWER THEM 3 Solve the problem 10 A satellte

PLEASE, PLEASE ANSWER THEM 3.

Solve the problem. 10 A satellte following the hyperbolic path shown in the picture turns rapidly at (0, 4) and then moves closer and closer to the line y 3x as it gets farther from the tracking station at the origin. Find the equation that describes the path of the rocket if the center of the hyperbola is at (0, 0) (0,4 \\Tracking station 10 2 x2 36 16 25 2 x2 16 36 25 100 16 16 100 (100)

Solution

center = (0,0)

vertex = ( 0 , 4)

distance between center and vertex = a = 4

standard equation is given by

y^2 / a^2 - x^2 / b^2 = 1

y^2 / 16 - x^2 / b^2 = 1

asymptote of hyperbola is y = 10/3 x

y = a/b x

10/3 = 4/b

b = 12 /10 = 6/5

b^2 = 36 / 25

hence , equation becomes

y^2 / 16 - x^2 / (36/25) = 1

or

y^2 / 16 - 25x^2 / 36 = 1

option 2 is correct