Question

A circle is represented by the equation below:

Answer 1

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.

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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:

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

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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).

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Radius:

Again, comparing both equations:

$r^2 = 49$

$r = \sqrt{49} = 7$

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

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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