Answer:
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.