SAT-Style: Circle Equation Problems

SAT Math · Axiom Academy

SAT-Style: Circle Equation Problems Three worked problems in the exact format the Digital SAT uses On the SAT, circle questions almost always test one of three moves: completing the square to find the center and radius, building an equation from a center and radius (often with a radical radius), or working from a diameter . Here is one fully-worked example of each. Example 1 — Complete the Square Half of 10 is 5 (square 25 ); half of -4 is -2 (square 4 ). Add to both sides: Example 2 — Build the Equation (Radical Radius) (x - h)^2 + (y - k)^2 = r^2 with h = -3 , k = 4 : Every SAT circle problem reduces to finding two things — the center (h, k) and the radius r — and then placing them into (x - h)^2 + (y - k)^2 = r^2 . Match the clue to the move: Expanded equation? Complete the square. Center and radius given? Plug in — and square the radius. A diameter or two points? Midpoint for the center, half-distance for the radius.

This is the written version of the interactive lesson above. See the full SAT Math course.