A circle is represented by the equation below: (x − 5)2 + (y + 7)2 = 49

Which statement is true?

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

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 and radius r, is given by:

In this question:

The following equation of a circle is given:

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Center:

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

As for y:

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

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Radius:

Again, comparing both equations:

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:

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step-by-step explanation:

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step-by-step explanation:

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