Respuesta :
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 [tex](x_0,y_0)[/tex] and radius r, is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this question:
The following equation of a circle is given:
[tex](x - 5)^2 + (y + 7)^2 = 49[/tex]
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Center:
We have to compare the two equations, to find [tex]x_0[/tex] and [tex]y_0[/tex]. So
[tex]x - x_0 = x - 5[/tex]
[tex]-x_0 = -5[/tex]
[tex]x_0 = 5[/tex]
As for y:
[tex]y - y_0 = y + 7[/tex]
[tex]-y_0 = 7[/tex]
[tex]y_0 = -7[/tex]
Thus, the circle is centered at (5,-7).
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Radius:
Again, comparing both equations:
[tex]r^2 = 49[/tex]
[tex]r = \sqrt{49} = 7[/tex]
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: https://brainly.com/question/24307696
