# Answer to Question #5790 in Geometry for maria prettymaths

Question #5790

My Dear Expert Sir what is the easy way to derive formula of a circle.

Expert's answer

what is the easy way to derive formula of a circle?

The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.

Remember that a circle is a locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle.

On the coordinate plane, the formula becomes

(x-x0)² + (y-y0)² = R²,

where (x0;y0) is a the center of the circle. Here we used the Pythagorean theorem.

& & & & & & & (x,y) - point of a circle

& & & & & & & & /|

& /& |

& & & & & & R / & |

& & / & & |

& /& & |

& & & & & /____|

& (x0,y0)

The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.

Remember that a circle is a locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle.

On the coordinate plane, the formula becomes

(x-x0)² + (y-y0)² = R²,

where (x0;y0) is a the center of the circle. Here we used the Pythagorean theorem.

& & & & & & & (x,y) - point of a circle

& & & & & & & & /|

& /& |

& & & & & & R / & |

& & / & & |

& /& & |

& & & & & /____|

& (x0,y0)

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