Question

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer 1

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.