Find the standard equation of a circle (x-h)² + (y-k)² = r² given center and radius.
Circle Parameters
Standard Equation
Equation(x - 2)² + (y + 3)² = 25
General Formx² + y² - 4x + 6y - 12 = 0
Equation of a Circle
A circle is defined as the set of all points (x, y) that are a fixed distance (radius r) from a fixed point (center (h, k)). The standard equation is derived from the Pythagorean theorem/distance formula.
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Pro Tips
If the center is at the origin (0,0), the formula simplifies to x² + y² = r².
The General Form looks like x² + y² + Dx + Ey + F = 0.
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Fun Facts
"A circle is a special case of an ellipse where the two foci coincide."
"Archimedes approximated Pi by inscribing and circumscribing polygons around a circle."
