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

Answer:

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 $r$ 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.

Answer 2

Answer:

1,4

Step-by-step explanation: