ACT Math Practice Question #1202 (Medium (31)) | Test Citadel
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ACT Math Difficulty: Medium (31)

Digital ACT Math Practice Question #1202

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An ellipse centered at the origin in the standard $(x,y)$-coordinate plane has a major horizontal axis of length $14$ and a minor vertical axis of length $8$. What is the distance between the two foci of this ellipse?
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Remember that the focal distance formula for ellipses is $c = \sqrt{a^2 - b^2}$. The total distance between foci is $2c$. Since $c = \sqrt{49 - 16} = \sqrt{33}$, the total distance is $2\sqrt{33}$.

Masterclass Solution & Distractor Trap Analysis

The semi-major axis is $a = 14/2 = 7$ and the semi-minor axis is $b = 8/2 = 4$. In an ellipse, the focal distance from the center $c$ satisfies $c^2 = a^2 - b^2 = 7^2 - 4^2 = 49 - 16 = 33$, so $c = \sqrt{33}$. The distance between the two f...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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