Digital SAT Math Practice Question #962
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Complete the square for the \( x \) and \( y \) terms to identify the center \( (h, k) \) of the circle. Then observe the relationship between the center and the given point of tangency.
Desmos Shortcut: Type the original circle equation directly into Desmos: \( x^2 + y^2 - 10x + 4y - 20 = 0 \). Desmos graphs implicit relations effortlessly! Plot the point \( (5, 5) \) to immediately see that the tangent line is a flat horizontal line.
First, complete the square to write the circle in standard form \( (x - h)^2 + (y - k)^2 = r^2 \): \[ (x - 5)^2 + (y - -2)^2 = 49 \] The center of the circle is \( (5, -2) \) and the radius is \( 7 \). The point of tangency is \( P(5, 5) \)...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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