Answer: The radius of the circle is 3 units, the standard form of the equation is (x – 1)² + y² = 3, and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Explanation:
To determine the properties of the circle whose equation is x^2 + y^2 - 2x - 8 = 0, we can complete the square as follows:
x^2 - 2x + y^2 - 8 = 0
(x^2 - 2x + 1) + y^2 = 9
(x - 1)^2 + y^2 = 3^2
The last expression is in the standard form of the equation for a circle with center (1, 0) and radius 3. Therefore, the center of the circle is (1, 0), which does not lie on either the x-axis or the y-axis.
We can also see that the radius of the circle is 3 units because the equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.
Finally, we can see that the radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9, which is the equation of a circle with center (0, 0) and radius 3.