SAT Math Practice Question #447 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #447

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

In the \( xy \)-plane, the circle given by the equation \[ x^2 + y^2 - 6x + 8y = 0 \] intersects the positive x-axis at point \( A \). A line tangent to the circle at point \( A \) intersects the y-axis at point \( C \). What is the area of triangle \( OAC \), where \( O(0,0) \) is the origin?
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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 rigorous, multi-step geometry and coordinate plane problem. We need to find the circle's properties, the equation of a tangent line, and finally the area of a triangle. Step 1: Find the center and x-intercepts of the circle. To fi...

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

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