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

Answer: To answer this question, we can start by putting the given equation in standard form by completing the square:

x² + y² – 2x – 8 = 0

(x² – 2x + 1) + y² = 9

(x – 1)² + y² = 3²

So, the center of the circle is (1, 0) and the radius is 3 units. This means that the statements that are true are:

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The standard form of the equation is (x – 1)² + y² = 3.

The statement "The center of the circle lies on the y-axis" is false, since the center is (1, 0) and it lies on the x-axis. The statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is also false, since the radius of the given circle is 3 units and the radius of the circle x² + y² = 9 is 3 units as well.

Explanation: