SAT Math Practice Question #238 (Hard (665)) | Test Citadel
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SAT Math Difficulty: Hard (665)

Digital SAT Math Practice Question #238

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: \[ x^2 + y^2 - 10x + 6y + 9 = 0 \] If this circle is translated 2 units to the right and 3 units down, what is the radius of the resulting circle?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
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

This is a fantastic geometry question that combines completing the square with a conceptual test on transformations. Let's break it down. First, a massive conceptual shortcut: **Translating (sliding) a circle across the coordinate plane shi...

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

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