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

The radius of the circle is 3 units, the center of the circle lies on the x-axis and the standard form of the equation is (x – 1)² + y² = 3.

- Q: What is the center of the circle? A: To find the center, we need to complete the square for both x and y terms. x2 - 2x + y2 = 8 => (x - 1)² + y2 = 9. So, the center of the circle is at (1,0).
- Q: What is the radius of the circle? A: The equation of the given circle is (x - 1)² + y² = 3². Therefore, the radius is 3 units.
- Q: Is the center of the circle lying on x-axis? A: Yes.
- Q: Is the center of the circle lying on y-axis? A: No.
- Q: Is the standard form of the equation of the circle (x – 1)² + y² = 3? A: Yes.
- Q: What is the radius of the circle whose equation is x² + y² = 9? A: The radius of the circle x² + y² = 9 is 3.