Question

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

Answer 1

Placing the equation of the circle in standard-form, the correct statements are given as follows:

• 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.

What is the equation of a circle?

The equation of a circle of center $(x_0, y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In this problem, the equation is:

x² + y² - 2x - 8 = 0.

In standard-form:

x² - 2x + y² = 8

(x - 1)² + y² = 8 + 1²

(x - 1)² + y² = 9

Center of (1,0), on the x-axis, radius of 3, hence the correct statements are:

• 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.

More can be learned about the equation of a circle at brainly.com/question/24307696
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