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

Therefore, the true statements are:

The radius of the circle is 3 units.

The standard form of the equation is (x - 1)^2 + y^2 = 9.

The radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9.

Explanation:

To determine which statements are true about the given circle, we can start by putting the equation in standard form:

x^2 + y^2 - 2x - 8 = 0

Completing the square for the x-terms, we get:

(x^2 - 2x + 1) + y^2 - 9 = 0

(x - 1)^2 + y^2 = 9

Now we can see that the center of the circle is (1, 0) and the radius is 3 units.

Based on this information, the following statements are true:

The radius of the circle is 3 units.

The center of the circle does not lie on the x-axis, so the statement "The center of the circle lies on the x-axis" is false.

The center of the circle lies on the y-axis, so the statement "The center of the circle lies on the y-axis" is false.

The standard form of the equation is (x - 1)^2 + y^2 = 9, which is true.

The radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9, which is true.