Question

A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?

y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x

Answer 1

The equations that represent the boundaries of the light are y = -12/5 and y = 12/5

How to determine the boundaries?

The equation is given as:

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

Subtract 3600 from both sides

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

Divide both sides by -3600

$\frac{y^2}{25} - \frac{x^2}{144} = 1$

Express as squares

$\frac{y^2}{5^2} - \frac{x^2}{12^2} = 1$

The asymptotes' equation are then represented as:

$y =\pm \frac{12}{5}$

Hence, the equations that represent the boundaries of the light are y = -12/5 and y = 12/5

Read more about hyperbolas at:

https://brainly.com/question/13955041

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Answer 2

The equations that represent the boundaries of the light are y = -12/5 and y = 12/5.

What is Hyperbola?

A hyperbola, a type of smooth curve lying in a plane, has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Here, the given equation:

     25x² – 144y² + 3,600 = 0

    25x² - 144y² = -3600

Divide whole equation by (-3600), we get

     -x²/144 + y²/25 = 1

      y²/5² - x²/12² = 1

The asymptotes' equation are then represented as:

     y = ± 12/5x

Thus, y equals twelve fifths x and y equals negative twelve fifths x.

Learn more about Hyperbola from:

https://brainly.com/question/12919612

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