Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range.

\\x^2 + y^2 = 36\\

what is the center of the circle?

the circle is centered at the point (0,0).
(type an ordered pair.)

what is the radius of the circle?

the radius of the circle is .
(type an integer or a fraction.)

Explanation:

Identify the standard form

Using the Standard Form of Circle knowledge point, we compare the given equation to the standard equation of a circle centered at \((h, k)\) with radius \(r\):

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

Determine the center

Using the Equation of a Circle knowledge point, we rewrite the given equation \(x^2 + y^2 = 36\) as:

$$(x - 0)^2 + (y - 0)^2 = 6^2$$

This shows the center \((h, k)\) is \((0, 0)\).

Determine the radius

Using the Standard Form of Circle knowledge point, we identify \(r^2 = 36\). Since radius must be positive:

$$r = \sqrt{36} = 6$$

Answer:

What is the radius of the circle?

The radius of the circle is <blank>6</blank>