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tatyana61 [14]
3 years ago
6

A circle is represented by the equation below:

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

To solve this question, we need to interpret the equation of a circle, to find that:

The circle is centered at (5, −7) and has a radius of 7.

-------------------

Equation of a circle:

The equation of a circle, with center (x_0,y_0) and radius r, is given by:

(x - x_0)^2 + (y - y_0)^2 = r^2

In this question:

The following equation of a circle is given:

(x - 5)^2 + (y + 7)^2 = 49

-------------------

Center:

We have to compare the two equations, to find x_0 and y_0. So

x - x_0 = x - 5

-x_0 = -5

x_0 = 5

As for y:

y - y_0 = y + 7

-y_0 = 7

y_0 = -7

Thus, the circle is centered at (5,-7).

-------------------

Radius:

Again, comparing both equations:

r^2 = 49

r = \sqrt{49} = 7

So the radius is 7(diameter 2*7 = 14).

-------------------

With the center and radius found, the correct option is:

The circle is centered at (5, −7) and has a radius of 7.

A similar example is found at: brainly.com/question/24307696

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