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:

Convert from general to standard form

`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`

Hence, the center of the circle is (1,0) which lies on the x-axis, and has a radius of 3 units.