Question

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.
On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.

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 7-foot radius.

Answer 1

Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²

The equation of a circle.

Mathematically, the equation of a circle can be derived by using Pythagorean theorem;

x² + y² = r²

Where:

• h and k represents the coordinates at the center.

• r is the radius of a circle.

After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:

(x - h)² + (y - k)² = r²

Read more on circle here: brainly.com/question/14078280

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