Question

A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x^(2)-144y^(2)+3600=0, which of the following equations represents the boundaries of the light? y=(5)/(12)x and y=-(5)/(12)x y=(5)/(13)x and y=-(5)/(13)

Answer 1

The equations representing the boundaries of the light emitted by the table lamp in the shape of a hyperbola are y = (5/12)x and y = -(5/12)x.

Step-by-step explanation:

The equation of the hyperbola is given by 25x^2 - 144y^2 + 3600 = 0. To find the boundaries of the light, we need to solve for y in terms of x. Let's solve the given equation for y:

25x^2 - 144y^2 + 3600 = 0

-144y^2 = -25x^2 + 3600

y^2 = (25/144)x^2 - 25

y = ±sqrt((25/144)x^2 - 25)

So, the equations representing the boundaries of the light are y = (5/12)x and y = -(5/12)x.