Question

question 8 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 x - coordinate b. the radius c. the y - coordinate d. the origin

Explanation:

Step1: Recall circle - equation formula

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 of the circle.

Step2: Analyze the effect of changing values

If we want to make the circle bigger or smaller, we change the value of \(r\). When \(r\) increases, the circle gets bigger, and when \(r\) decreases, the circle gets smaller. The \(x\) - coordinate and \(y\) - coordinate of the center of the circle (which is at the origin \((0,0)\) here) do not change the size of the circle. The origin itself is a fixed point and does not affect the size of the circle.

Answer:

B. The radius