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In the hyperbola, 42 − 92 = 36, the foci are located at:

a. (±6,0)
b. (0,±6)
c. (±√13, 0)
d. (0, ±√13)
e. (0,0)

1 Answer

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Final answer:

Assuming the hyperbola equation is corrected to (x²/42) - (y²/92) = 1, the foci are located at approximately (±√13, 0) after using the formula c = √(a² + b²) to calculate their position.

Step-by-step explanation:

The given equation appears to represent a hyperbola, but it seems to have a typo, as hyperbolas have the general equation ℚ(x - h)²/a² - ℚ(y - k)²/b² = 1, where a and b are the lengths of the semi-major axis and semi-minor axis respectively, and (h, k) is the center of the hyperbola. Assuming a corrected version of the equation is (x²/42) - (y²/92) = 1, which is in standard form, we can find the distance of the foci from the center by the formula c = √(a² + b²). For this hyperbola, a² = 42 and b² = 92. Thus, c = √(42 + 92) = √(4 + 81) = √85. Since a hyperbola opens along the x-axis in this case, the foci are located at (±√85, 0), which is roughly (±√13, 0) when approximated.

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