Question

question 9 of 10
when you make the circle bigger or smaller, which number of the standard
equation for a circle centered at the origin changes?

a. the y - coordinate
b. the radius
c. the x - coordinate
d. the origin

Explanation:

Step1: Recall the standard equation of a circle

The standard equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \((x,y)\) is a point on the circle and \(r\) is the radius.

Step2: Analyze the effect of changing the circle's size

When we make the circle bigger or smaller, we are changing its size. In the equation \(x^{2}+y^{2}=r^{2}\), the value that determines the size of the circle (distance from the center to any point on the circle) is \(r\) (the radius). The \(x\) - coordinate and \(y\) - coordinate represent points on the circle, and the origin \((0,0)\) is the center which remains fixed as the problem states the circle is centered at the origin.

Answer:

B. The radius