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

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.