Question

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

Answer 1

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
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& & & & & & R / & |
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& (x0,y0)