In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle? (h + x)2 + (k + y)2 = r2 (x – h)2 + (y – k)2 = r2 (k + x)2 + (h + y)2 = r2 (x – k)2 + (y – h)2 = r2

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle the equation of the new circle

(x – h)2 + (y – k)2 = r2

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oeerivona oeerivona · Answer 2 · 2022-03-23T16:58:34+01:00

Based on Pythagorean theorem, and the location of the center of the

circle, (h, k), the equation of the circle is represented by the option;

(x - h)² + (y - k)² = r²

How can the equation of the circle be found?

The general form of the equation of the circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The center of the circle

r = The radius of the circle

A description of the equation of the circle is as follows;

With regard to a location on the edge (circumference), of the circle, (x, y),

where, the center of the circle is (h, k), by Pythagorean the sum of the

square of the length of the horizontal side, (x - h), and the square of the

vertical side (y - k), of the right triangle formed gives the square of the

radius of the circle.

Therefore, the equation of the new circle can be represented by the equation;

(x - h)² + (y - k)² = r²

The above equation is the general form of the equation of a circle.

Learn more about the equation of a circle here:

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