Digital SAT · Math · Geometry and Trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Circle questions come in two kinds. The first kind is about parts of a circle. An arc is a fraction of the circumference and a sector is the same fraction of the area. The fraction is the central angle divided by the full turn: 360° or 2π radians.
The second kind is about the equation of a circle in the xy-plane. In standard form you can read the center and the radius directly. If the equation is expanded, complete the square in x and in y to get back to standard form.
Remember that the right-hand side of the standard form is the radius squared, not the radius.
Getting the signs of the center wrong or forgetting to take the square root. (x + 2)2 + (y − 7)2 = 49 has center (−2, 7) and radius 7, not center (2, −7) or radius 49.
Answer: Center (−2, 7), radius 7
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