SAT Math Practice Question #292 (Hard (770)) | Test Citadel
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SAT Math Difficulty: Hard (770)

Digital SAT Math Practice Question #292

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

A circle in the xy-plane has the equation \( x^2 + y^2 - 6x + 8y = c \), where \( c \) is a constant. If the circle intersects the y-axis at exactly one point, what is the value of \( c \)?
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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 an elite-level geometry and algebra synthesis question. When a circle intersects the y-axis at *exactly one point*, it means the circle is perfectly tangent to the y-axis. Let's figure out what that means geometrically by putting th...

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

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