Question

When you make the circle bigger or smaller, which number of the standard equation for the circle centered at the origin changes?

A. the x coordinate
B. the y coordinate
C. the radius
D. the origin

Answer 1

Option (C) is correct,

when we make the circle bigger or smaller we will change its radius.

Explanation:

A circle with standard equation,
`(x-h)^2 + (y-k)^2 = r^2` where (h, k) is the center and "r" being the radius.

We have to determine out of given options which number of the standard equation for the circle centered at the origin changes when you make the circle bigger or smaller.

Given : Circle centered at the origin then (h , k ) becomes (0, 0)

Thus, equation of circle becomes,

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

Substitute h = 0 and k = 0 , we get,

`\Rightarrow (x-0)^2 + (y-0)^2 = r^2`

`\Rightarrow x^2 + y^2 = r^2`

Since, x and y coordinates depends on radius.

Thus when we make the circle bigger or smaller we will change its radius.

Thus, option (C) is correct,

Answer 2

I think the correct answer from the choices listed above is option C. When you make the circle bigger or smaller, it is the radius of the standard equation for the circle centered at the origin changes. Hope this answers the question. Have a nice day.