SAT Math: Equation of a Circle in the Coordinate Plane
22+ practice questions in Praczo
The concept, explained
- 1
Standard form: (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
- 2
Read the center directly from the equation — watch the signs: (x − 3)² has center x = 3; (x + 3)² has center x = −3.
- 3
The radius is the square root of the right-hand side: if the equation equals 25, r = 5.
- 4
To find the equation given the center and a point on the circle, substitute to find r² using the distance formula.
- 5
If the equation is not in standard form, complete the square on x and y to convert it.
- ✗ Reading the center incorrectly: (x + 2)² means h = −2, not +2.
- ✗ Taking the right side as r rather than r² — always take the square root.
SAT-style practice
What is the center of the circle given by (x − 4)² + (y + 1)² = 36?
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