Question

1. find the center and radius of the circle with equation ((x + 8)^2 + (y + 3)^2 = 49).

center (-8, -3); radius 7
center (8, 3); radius 49
center (8, 3); radius 7
center (-8, -3); radius 49

Explanation:

Step1: Match to circle standard form

The standard equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Identify center coordinates

Compare $(x+8)^2 + (y+3)^2 = 49$ to the standard form:
$x+8 = x - (-8)$, so $h=-8$; $y+3 = y - (-3)$, so $k=-3$.
Center: $(-8, -3)$

Step3: Calculate the radius

$r^2=49$, so $r=\sqrt{49}=7$

Answer:

center (-8, -3); radius 7