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

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Explanation:

x² + y² - 2x - 8 = 0

x² - 2x + y² = 8

Complete the square in x.

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

Center: (1, 0); radius: 3

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE