Mathematics, 15.07.2020 02:01 gingerham1

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.

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

The standard equation of a circle is expressed as:

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

Centre is (-g, -f)radius = √g²+f²-C

Given a circle whose equation is x^2 + y^2 - 2x - 8 = 0.

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

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

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

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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Answer from: yorbal6109

The statements 1 and 4 are true.

Step-by-step explanation:

In order to quickly visualize the center and radius of the circle we can manipulate the given equation in such a way that it changes to the standard form.

$x^2 + y^2 - 2x - 8 = 0\\x^2 - 2x + y^2 = 8\\(x^2 - 2x + 1) + y^2 = 8 + 1\\(x - 1)^2 + y^2 = 9$

Now that the equation is its standard form we can compare it to the standard form formula to determine the center and radius of the circle:

(x - x_c)^2 + (y - y_c)^2 = r^2

Where (x_c,y_c) are the coordinates of the center of the circle and is the radius of the circle. Therefore the circle we were given has center in (1,0) and radius $r = \sqrt{9} = 3$ . With this in mind we can analyze each statement.

1. The radius of the circle is 3 units. This statement is correct.

2. The center of the circle lies on the y-axis. This statement is false, since the center of the circle has the coordinates (1,0) it means that it actually lies in the x-axis.

3. The standard form of the equation is (x - 1)² + y² = 3. This is false the correct standard equation is (x - 1)² + y² = 9.

4. The radius of the circle is the same as the radius of the circle who's equation is x² + y² = 9. This statement is correct, the radius is given by the square root of the constant on the right side of the equation, therefore the radius of both circle is 3.

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Answer from: Quest

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

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