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QuizMultiple Choice

Applications of Conics — Quiz

Question 1 • Precalculus

A castle entrance has walls that can be modeled by the equation the fraction with numerator x squared and denominator 10 squared minus the fraction with numerator y squared and denominator 30 squared is equal to 1 with units in feet. How wide is the entrance where the walls are closest together?

Answer
A
20 ft
B
30 ft
C
60 ft
D
10 ft

Explanation

The equation is x²/10² − y²/30² = 1, a horizontal hyperbola centered at the origin. Its closest points are the vertices, where y = 0 and x = ±10, so the distance between the walls there is 10 − (−10) = 20 feet. The entrance is 20 ft wide.

AI-written and checked against the verified answer.

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