Question

zain draws a circle with radius r and center (h, k) in the coordinate plane. he places the point (x, y) on the circle. how can zain use his drawing to derive the general equation of a circle in standard form? use the drop - down menus to explain your answer.

Explanation:

Step1: Apply distance formula

The distance between center $(h,k)$ and point $(x,y)$ is the radius $r$. Using the distance formula:
$$r = \sqrt{(x-h)^2 + (y-k)^2}$$

Step2: Square both sides

Eliminate the square root by squaring each side:
$$r^2 = (x-h)^2 + (y-k)^2$$

Answer:

The standard form of the circle's equation is $\boldsymbol{(x-h)^2 + (y-k)^2 = r^2}$, derived by applying the distance formula between the center $(h,k)$ and any point $(x,y)$ on the circle, then squaring both sides to remove the square root.