Question

Which graph represents a circle with equation x2 + y2 = 9

Answer 1

Answer: The correct option is (B). Its image is attached below.

Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:

`x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by

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

From equation (i), we have

`x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.`

Comparing the above equation with the standard equation of a circle, we get

Center, (h, k) = (0, 0) and radius, r = 3 units.

We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.

We see that the graph of the circle is same as the one provided in option (B).

Thus, option (B) is CORRECT.

Answer 2

The basic form of the equation of a circle is:
x^2+y^2=r^2
where r^2 is the radius squared.

Looking at your equation, x^2+y^2=9, the radius is 3 (sqrt of 9 is 3)

Therefore, the graph B would be correct since the radius of the circle at all points is 3.

Hope I helped :)