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Give the center and radius of the circle described by the
equation and graph the equation. Use the graph to identify
the relation’s domain and range.

What is the center of the circle?
The circle is centered at the point
(Type an ordered pair.)

Ask by Salazar Edwards. in the United States
Mar 31,2025

Solución de inteligencia artificial de Upstudy

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The center of the circle is at .

Solución

  1. The given equation of the circle is
  2. The standard form of a circle’s equation is
    where is the center and is the radius.
  3. By comparing the given equation with the standard form, we see that it can be rewritten as
  4. Therefore, the center is
    and the radius is
  5. For the graph of the circle:
    • The circle is centered at with radius .
    • The circle touches the points , , , and .
  6. The domain of the circle (the -values) is all points for which
    and the range (the -values) is all points for which
The circle is centered at the point .

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The Deep Dive

The equation is a standard form of a circle’s equation, which can be represented as where is the center and is the radius. Here, we can see that the center of the circle is at the point (0, 0) and the radius is .
To graph the circle, you can plot points that are 7 units away from the center in all directions: up to (0, 7), down to (0, -7), left to (-7, 0), and right to (7, 0). The domain of the relation is and the range is also , since the circle touches these points on the x and y axes.

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