SAT and ACT math terms · SAT Math, ACT Math
Equation of a circle
Equation of a circle: The equation (x − h)² + (y − k)² = r² describes a circle with center (h, k) and radius r.
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What it means
If a circle's equation is given in expanded form, complete the square for x and y to find the center and radius. Related formulas: circumference 2πr, area πr², arc length (θ/360) × 2πr, and sector area (θ/360) × πr² for a central angle θ in degrees.
A tangent line to a circle is perpendicular to the radius at the point of tangency.
Example
x² + y² − 6x + 4y = 12 becomes (x − 3)² + (y + 2)² = 25, a circle with center (3, −2) and radius 5.
On the exam
Both tests ask about circle equations, arcs and sectors.