The appropriate expression is y equals five twelfths x and y equals negative five twelfths x. Option A
How do we solve for the appropriate expression?
To find the expression, we first need to rewrite the given equation of the hyperbola in terms of y:
25x² - 144y² + 3,600 = 0
25x² - 144y² = - 3,600
(25x²/- 3,600) - ( 144y²/- 3,600) = 1
x²/25 - y²/144 = 1
x²/-25 - y²/-144 = 1
y = ±(b/a)x
In this case, a² =144 and b² =25, thus a=12 and b=5. The slopes of the asymptotes are ± 5/12
y = (5/12)x
y = (5/12)x
Full 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