To determine which statements are true, we can first rewrite the given equation into standard form by completing the square:
x2 + y2 – 2x – 8 = 0
(x2 - 2x) + y2 - 8 = 0
(x - 1)2 + y2 = 9
From this, we can see that the center of the circle is at the point (1, 0), which lies on the x-axis. Therefore, the statement "The center of the circle lies on the x-axis" is true, but "The center of the circle lies on the y-axis" is false.
The radius of the circle is sqrt(9) = 3 units, so the statement "The radius of the circle is 3 units" is true. Additionally, we can see that the standard form of the equation is (x – 1)² + y² = 3, so the statement "The standard form of the equation is (x – 1)² + y² = 3" is also true.
Finally, the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is true, since both circles have a radius of 3 units. Therefore, the three true statements 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.