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

1) The radius of the circle is 3 units.

2) The center of the circle lies on the x-axis.

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

Explanation:

`x^2+y^2-2x-8=0\\x^2-2x-8+y^2=0\\x^2-2x-8+9+y^2=0+9\\x^2-2x+1+y^2=9\\(x-1)^2+y^2=9`

By completing the square, we can see that the circle has its center at (1,0) and that its radius is 3 units. Thus, the 1st, 2nd, and 5th answers are all true.