Question

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

Answer 1

Considering the given equation of the circle, the true statements are given as follows:

• The radius of the circle is of 3 units.

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

• The circle has the same radius as the circle with equation 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:

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

The equation given is:

x2 + y² - 2x - 8 = 0.

Completing the squares, the equation is given as follows:

(x - 1)² + y² = 8 + 1

(x - 1)² + y² = 9.

Researching the problem on the internet, the true statements are:

• The radius of the circle is of 3 units.

• The center of the circle lies on the x-axis($y_0 = 0$).

• The circle has the same radius as the circle with equation x² + y² = 9.

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

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