Question

the equation of a circle is given in standard form. complete parts a through c to follow the step by step process to sketch the graph of the circle.$(x + 4)^2 + (y + 6)^2 = 49$the radius is 7(simplify your answer. type an exact answer, using radicals as needed.)b) sketch the graph of the circle.use the graphing tool to graph the circlec) determine the x- and y-intercepts of the circle. select the correct choice and, if necessary, fill in the answer box within your choicea. the x-intercept(s) is/are $x =$(use a comma to separate answers as needed. type an exact answer, using radicals as needed.)b. there is no x-intercept.

Explanation:

Step1: Find x-intercepts (set y=0)

Substitute $y=0$ into the circle equation:
$$(x+4)^2 + (0+6)^2 = 49$$

Step2: Simplify the equation

$$(x+4)^2 + 36 = 49$$
$$(x+4)^2 = 49 - 36 = 13$$

Step3: Solve for x

$$x+4 = \pm\sqrt{13}$$
$$x = -4 \pm\sqrt{13}$$

Step4: Find y-intercepts (set x=0)

Substitute $x=0$ into the circle equation:
$$(0+4)^2 + (y+6)^2 = 49$$

Step5: Simplify the equation

$$16 + (y+6)^2 = 49$$
$$(y+6)^2 = 49 - 16 = 33$$

Step6: Solve for y

$$y+6 = \pm\sqrt{33}$$
$$y = -6 \pm\sqrt{33}$$

Answer:

For x-intercepts:

A. The x-intercept(s) is/are $x = -4+\sqrt{13}, -4-\sqrt{13}$

For y-intercepts:

The y-intercept(s) is/are $y = -6+\sqrt{33}, -6-\sqrt{33}$

(Note: The graph is centered at $(-4, -6)$ with radius 7, which matches the provided grid sketch.)