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 center of the circle lies on the x-axis

The radius of the circle is 3 units.

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

How to determine the statements

The standard equation of a circle is expressed as:

$x^2 + y^2 + 2gx + 2fy + C = 0$

Where

• Centre is (-g, -f)

• radius = √g²+f²-C

Given a circle whose equation is

Let's get the center of the circle

2gx = -2x

2g = -2

We have that;

g = -1

Similarly, 2fy = 0

given that

f = 0

Centre = (-(-1), 0) = (1, 0)

This explains that the center of the circle lies on the x-axis

We move further to the radius

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9

= 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

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

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