Circle

Pre-Calculus — 1ˢᵗ Semester, Midterm

circle

set of all points in a plane that are equidistant from a given point called the center

center

fixed point of a circle

radius

constant distance from the center

x² + y² = r²

standard form of the equation of a circle with radius r and center at (0, 0)

(x - h)² + (y - k)² = r²

• center-radius form

• standard form of the equation of a circle with radius r and center at (h, k)

Ax² + By² + Dx + Ey + F = 0

general form of the equation of a circle

squaring the binomials

writing the equation of a circle in general form

completing the square

determining the center and radius of each circle in general form

(x₁ + x₂) / 2, (y₁ + y₂) / 2

• midpoint formula

• given the endpoints of the diameter, determining the center

1/2 √(x₂ - x₁)² + (y₂ - y₁)²

• distance formula

• given the endpoints of the diameter, divide by 2 to determine the radius