Circle Equations and Graphing
Master the standard and general forms of circle equations, centers, radii, and completing the square.
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Questions Covered in This Set
8 cards to master
What is the standard form equation of a circle?
(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius
What are the center and radius of (x - 3)² + (y + 2)² = 25?
Center: (3, -2), Radius: 5
What is the general form of a circle equation?
x² + y² + Dx + Ey + F = 0
How do you complete the square for x² + 6x?
Take half the coefficient of x (6/2 = 3), square it (9), and add it: (x + 3)²
What is a circle in geometric terms?
The set of all points in a plane equidistant from a fixed point (the center)
What is the equation of a circle centered at the origin with radius r?
x² + y² = r²
In (x - h)² + (y - k)² = r², why is the sign opposite the center coordinate?
Because the form is (x - h), the center's x-coordinate is h, not -h
What does it mean if r² ≤ 0 after completing the square?
Either a single point (r² = 0) or no real circle exists (r² < 0)
