SAT Math Practice Question #530 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #530

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

A line \( L \) is tangent to the parabola \( y = x^2 \) at the point \( (2, 4) \). A circle is tangent to line \( L \) at the point \( (2, 4) \) and is also tangent to the \( x \)-axis. If the center of the circle is \( (h, k) \) and \( k > 0 \), what is the sum of all possible values 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)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This is a premier, multi-step coordinate geometry problem. Let's tackle it piece by piece. Step 1: Find the equation of the tangent line \( L \). The parabola is \( y = x^2 \). To find the slope of the tangent line at \( x = 2 \) without ca...

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

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