Question

write the standard form of the equation of the circle with the given center and radius.

center \\((0,0)\\), \\(r = 3\\)

the equation for the circle in standard form is
(simplify your answer.)

Explanation:

State the standard form equation of a circle

The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:

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

Substitute the given center and radius

Substitute the center \((h, k) = (0, 0)\) and radius \(r = 3\) into the standard form:

$$(x - 0)^2 + (y - 0)^2 = 3^2$$

Simplify the equation

Simplify the terms to obtain the final standard form:

$$x^2 + y^2 = 9$$

Answer:

The equation for the circle in standard form is <blank>\(x^2 + y^2 = 9\)</blank>
(Simplify your answer)