SAT Math Practice Question #2540 (Medium) | Test Citadel
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SAT Math Difficulty: Medium

Digital SAT Math Practice Question #2540

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In the equation $x^2 + y^2 + 4x - 10y + c = 0$, the circle has radius 6. What is $c$?
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Geometry & Trig Rule: Always sketch the triangle or circle and check for standard Pythagorean triples (3-4-5, 5-12-13, 7-24-25, 8-15-17).

Masterclass Solution & Distractor Trap Analysis

Complete square: $(x + 2)^2 + (y - 5)^2 = 4 + 25 - c = 29 - c$. Since $r^2 = 36$, $29 - c = 36 \implies c = -7$....

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

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