To determine which statements are true about the circle whose equation is x^2 + y^2 - 2x - 8 = 0:
First, we can rewrite the equation in standard form by completing the square:
x^2 - 2x + y^2 = 8
(x - 1)^2 + y^2 = 9
From this form, we can see that the center of the circle is at (1, 0), which is on the x-axis. Therefore, statement 2 is true.
The radius of the circle is the square root of the constant term in the standard form equation, which is 3. Therefore, statement 1 is false and statement 5 is true.
Finally, the equation of the circle is in standard form, and we can see that the squared term for y is positive, which means that the center of the circle cannot lie on the y-axis. Therefore, statement 3 is false.
In summary, the three true statements are:
- 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.
- The standard form of the equation is (x – 1)² + y² = 3.