Answer:
A, B, E
Explanation:
You want three true statements describing the circle whose equation is ...
x² + y² – 2x – 8 = 0
Graph
A graphing calculator can plot this equation for you. The result is attached.
We see that ...
- The radius of the circle is 3 units.
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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Additional comment
The standard form equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . center (h, k), radius r
Rearranging the given equation to this form, we have ...
(x -1)² +y² = 8 +1 = 9 . . . . . . . . r²=9 ⇒ r=3
This means the center is (1, 0), and the radius is 3. The point (1, 0) is on the x-axis.
The circle with equation x² + y² = 9 is centered at the origin and has radius 3.