SAT Math Practice Question #220 (Medium (635)) | Test Citadel
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SAT Math Difficulty: Medium (635)

Digital SAT Math Practice Question #220

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

The equation of a circle in the \( xy \)-plane is given by \( x^2 + 6x + y^2 - 8y = 11 \). What is the radius of the circle?
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Socratic AI Engine Step-by-Step Derivation
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Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

The SAT tests this concept constantly. To find the radius, we need to convert this expanded circle equation into the standard form of a circle: \( (x-h)^2 + (y-k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius. Let's...

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

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