SAT Math Practice Question #1274 (Hard (730)) | Test Citadel
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SAT Math Difficulty: Hard (730)

Digital SAT Math Practice Question #1274

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In the $xy$-plane, a circle with center $(4, -2)$ is tangent to the line $y = 3$. Which of the following equations represents this circle?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Desmos hack: Type $(x-4)^2 + (y+2)^2 = 25$ and $y = 3$ directly into Desmos. Look at the graph: the circle touches $y = 3$ at exactly one point $(4, 3)$. Instant verification.

Masterclass Solution & Distractor Trap Analysis

The standard equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$. The center is $(h, k) = (4, -2)$, so the equation begins $(x - 4)^2 + (y - (-2))^2 = (x - 4)^2 + (y + 2)^2$. Since the circle is tangent to the horizontal line $y = 3$, the...

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

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