Question

use the pythagorean theorem to derive the equation of a circle. move one answer to each box. (horizontal distance)^2+(vertical distance)^2 = radius^2

Explanation:

Step1: Define variables

Let the center of the circle be $(h,k)$ and a point on the circle be $(x,y)$. The horizontal distance is $x - h$ and the vertical distance is $y - k$, and the radius is $r$.

Step2: Apply Pythagorean theorem

By the Pythagorean theorem, $(x - h)^2+(y - k)^2=r^2$.

Answer:

$(x - h)^2+(y - k)^2=r^2$