Question

1. given: $(x + 4)^2 + y^2 = 64$

find the center c and the radius r.
a. $c=(4,0)$ $r = 64$
b. $c=(-4,0)$ $r = 8$
c. $c=(4,0)$ $r = 8$
d. $c=(-4,0)$ $r = 64$

1. the equation of a circle is given. $(x + 4)^2 + y^2 = 36$

which graph represents the circle?

1. jen needs to water the lawn in her backyard, so she decides to use a rotary sprinkler that sprays water in

a circle with 40 ft in diameter. she places the sprinkler in the center of her backyard, which is 12 ft west
and 30 ft north of the back door to her house.
the back door of her house is represented at the origin of the coordinate plane.
complete the sentences:
the equation of the circle is (select):
$(x + 30)^2 + (y - 12)^2 = 40^2$
$(x - 30)^2 + (y + 12)^2 = 20^2$
$(x + 12)^2 + (y - 30)^2 = 20^2$
$(x - 12)^2 + (y + 30)^2 = 40^2$
the northernmost point the sprinkler will reach is at (select):
$(0,18)$
$(0,40)$
$(-12,50)$
$(-12,70)$

1. given the circle with central at p. complete the equation of the circle.

select:
$\

$$\begin{cases}x - 2 \\\\ y - 2 \\end{cases}$$

+\

$$\begin{cases}x + 2 \\\\ y + 2 \\end{cases}$$

=\frac{4}{16}$
$\

$$\begin{cases}x = 3 \\\\ y = -3 \\end{cases}$$

+\

$$\begin{cases}x + 3 \\\\ y + 3 \\end{cases}$$

$

Explanation:

Step1: Ecuación general de un círculo

La ecuación general de un círculo es \((x - h)^2+(y - k)^2=r^2\), donde \((h,k)\) es el centro y \(r\) es el radio.

Step2: Identificar \(h\), \(k\) y \(r\) en la ecuación \((x + 4)^2+y^2=64\)

Reescribimos \((x + 4)^2+y^2=64\) como \((x-(-4))^2+(y - 0)^2 = 8^2\). Aquí, \(h=-4\), \(k = 0\) y \(r = 8\).

Answer:

B. \(C=(-4,0)\), \(r = 8\)