SAT Math Practice Question #437 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #437

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

In the \( xy \)-plane, the graph of the equation \( x^2 + y^2 - 12x + ky + 45 = 0 \) is a circle. If the circle is tangent to the y-axis, and \( k > 0 \), what is the value of \( k \)?
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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 beautiful, high-level coordinate geometry problem. To solve anything involving the equation of a circle on the SAT, your very first instinct must be to 'Complete the Square' to get it into standard form: \( (x - h)^2 + (y - k)^2 =...

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

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