SAT Circles study notes

The SAT can give a circle through a graph rather than in equation form. Find the center and radius from the labels, then use (x − h)² + (y − k)² = r². When the equation gives two roots, the position of the point in the figure can tell you which one works.

Worked example

The circle is centered at (−2, 1), passes through (3, 1), and has an upper point (1, k). What is k?

The radius is 5. Substitute (1, k) into (x + 2)² + (y − 1)² = 25: 9 + (k − 1)² = 25. Thus k − 1 = ±4. The point is above the center, so k = 5.

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