In the standard (x,y) coordinate plane, the graph of (x + 3)2 + (y + 5)2 = 16 is a circle. What is the circumference of the circle, expressed in coordinate units?

Question

In the standard (x,y) coordinate plane, the graph of (x + 3)2 + (y + 5)2 = 16 is a circle. What is the circumference of the circle, expressed in coordinate units?

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5 answers
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Answer 1

Jai answered
11 years ago

The given equation follows the general equation for circles, which is

(x - a)^2 + (y - b)^2 = r^2
where
(a,b) = the point where the center of the circle lies
r = radius
From the equation,
(x + 3)^2 + (y + 5)^2 = 16
r^2 = 16
r = 4 units
Recall that the circumference of a circle is given by
C = 2*pi*r
Substituting,
C = 2*3.14*2
C = 25.12 units

hope it helps~ :)

Answer 2

ㅤ answered
2 years ago

2 π r

You got r=4
Ans you substitute r=2

Answer 3

Clown Bot answered
1 year ago

Well, calculating the circumference of a circle can be a bit daunting, but don't worry, I'll clown around and make it fun for you!

First, let's identify the center of the circle. The equation (x + 3)^2 + (y + 5)^2 = 16 tells us that the center is at (-3, -5).

Now, we need to find the radius of the circle. The equation (x + 3)^2 + (y + 5)^2 = 16 is in standard form, which means the radius is the square root of the constant term, in this case, 16. So, the radius is √16 = 4.

To find the circumference, we'll use the formula C = 2πr. Plugging in the radius, we get C = 2π(4) = 8π.

Therefore, the circumference of the circle is 8π units. Happy clowning around with circles!

Answer 4

Step-by-Step Bot answered
1 year ago

To find the circumference of a circle, we can use the formula:

C = 2πr

In the given equation, we can see that the center of the circle is (-3, -5), and the radius is √16, which simplifies to 4.

Substituting the values into the formula, we get:

C = 2π(4)

C = 8π

Therefore, the circumference of the circle, expressed in coordinate units, is 8π.

Answer 5

Explain Bot answered
1 year ago

To find the circumference of a circle, you need to know its radius. In the given equation, the equation of the circle is in the form (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.

In this case, the equation is (x + 3)² + (y + 5)² = 16. Comparing it to the general form, we can determine that the center of the circle is at (-3, -5) and the radius is √16 = 4.

The circumference of a circle is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159.

Substituting the radius (r = 4) into the formula, we get:
C = 2π(4) = 8π.

Therefore, the circumference of the circle is 8π coordinate units.