Answer :
Let's analyze the given equation of the circle:
[tex]\[ (x + 7)^2 + (y + 7)^2 = 16 \][/tex]
This equation is in the standard form of a circle's equation [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
1. From the given equation, [tex]\((x + 7)^2 + (y + 7)^2 = 16\)[/tex], we can identify that [tex]\(h = -7\)[/tex] and [tex]\(k = -7\)[/tex] because the equation can be rewritten as:
[tex]\[ (x - (-7))^2 + (y - (-7))^2 = 16 \][/tex]
Therefore, the center of the circle is at [tex]\((-7, -7)\)[/tex].
2. The right-hand side of the equation is 16, which represents [tex]\(r^2\)[/tex], the square of the radius. This means:
[tex]\[ r^2 = 16 \][/tex]
3. To find the radius [tex]\(r\)[/tex], we take the square root of 16:
[tex]\[ r = \sqrt{16} \][/tex]
[tex]\[ r = 4 \][/tex]
Therefore, the radius of the circle is 4. The correct answer is:
B. 4
[tex]\[ (x + 7)^2 + (y + 7)^2 = 16 \][/tex]
This equation is in the standard form of a circle's equation [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
1. From the given equation, [tex]\((x + 7)^2 + (y + 7)^2 = 16\)[/tex], we can identify that [tex]\(h = -7\)[/tex] and [tex]\(k = -7\)[/tex] because the equation can be rewritten as:
[tex]\[ (x - (-7))^2 + (y - (-7))^2 = 16 \][/tex]
Therefore, the center of the circle is at [tex]\((-7, -7)\)[/tex].
2. The right-hand side of the equation is 16, which represents [tex]\(r^2\)[/tex], the square of the radius. This means:
[tex]\[ r^2 = 16 \][/tex]
3. To find the radius [tex]\(r\)[/tex], we take the square root of 16:
[tex]\[ r = \sqrt{16} \][/tex]
[tex]\[ r = 4 \][/tex]
Therefore, the radius of the circle is 4. The correct answer is:
B. 4
