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.

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

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

Explanation:

Convert the equation to standard form: (x-h)²+(y-k)²=r²:

x²+y²-2x-8=0 ⇒ (x²-2x+ 1 ) + y² = 8+ 1 ⇒ (x-1)²+y²=9

The center is at (1,0) and the radius is 3.