Applying the Pythagorean Theorem: Equation of the circle

One of the first applications that can be found in the Pythagorean theorem, is its use in determining the equation of a circle.

Metric relationship between the two legs of a right triangle are essentially the expression of the concept of Euclidean measure.

The points of a circle are equidistant from the center of the (O).

A circle is the locus of points in a plane equidistant from a fixed point and coplanar another call center in a constant amount called radio.(W)

To determine the equation of the circle analyze first the case in which it is found with its center at the origin of the reference system, to generalize to any position below the plane.

The distance of any point P(x,and) the circumference at its center O is equal to the radius R. In the figure is seen that the hypotenuse of a right triangle whose legs at the coordinates x and and Point P. Thus, applying the Pythagorean theorem:

If we shift the center of the circle to a point coordinate (Xo, I), As seen in Figure:

points will follow the circumference of the center distance R, but in this case the legs of the triangle are no longer coordinates, but the difference between them and the center. The new equation is:

We can develop this equation and grouping the coefficients and variables in an orderly, with what we:

Or simplify grouping

Being

Direct application therefore an important theorem in geometry.

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