Question

question 9 of 10
to find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures:
a. the distance from any point on the circle to the origin.
b. the distance from any point inside the circle to the origin.
c. the distance from the x - coordinate to the origin.
d. the distance from the circumference.

Explanation:

Step1: Recall circle equation concept

The standard - form equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius. The radius \(r\) is the distance from the origin \((0,0)\) to any point \((x,y)\) on the circle. We use the distance formula \(d = \sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}\). For a circle centered at the origin \((x_1,y_1)=(0,0)\) and a point \((x,y)\) on the circle, \(d=\sqrt{(x - 0)^{2}+(y - 0)^{2}}=\sqrt{x^{2}+y^{2}}\), and since \(d = r\) (radius), \(x^{2}+y^{2}=r^{2}\). The radius is the distance from the origin to any point on the circle.

Answer:

A. the distance from any point on the circle to the origin.