Question

Given the equation (x+3)^2+y^2=81, choose ALL correct answers.

a) The center of the circle would lie on the x-axis.
b) The center of the circle would lie on the y-axis.
c) The center of the circle would lie in a quadrant.
d) The radius is 9.
e) The radius is 40.5
f) The radius is 81
g) The diameter is 18.
h) The diameter is 81.
i) The diameter is 162.

Answer 1

The correct statements are:

- b) The center of the circle would lie on the y-axis.

- d) The radius is 9.

- g) The diameter is 18.

Step-by-step explanation:

The given equation
`\((x+3)^2+y^2=81\)` represents the equation of a circle in the coordinate plane. The general form of the equation for a circle with center (h, k) and radius
`\(r\) is \((x-h)^2 + (y-k)^2 = r^2\).`

Comparing this with the given equation, we can determine the properties of the circle:

- The center of the circle is (-3, 0), so it lies on the x-axis. Therefore, statement a) is incorrect, and statement b) is correct.

- The radius of the circle is the square root of 81, which is 9. Therefore, statement d) is correct, and statements e) and f) are incorrect.

- The diameter of the circle is twice the radius, so it is
`\(2 * 9 = 18\).`Therefore, statement g) is correct, and statements h) and i) are incorrect.

In conclusion, the correct statements are b), d), and g).

Answer 2

The center of the circle lies on the x-axis and the radius is 9. The correct options are a and d.

Step-by-step explanation:

The given equation represents a circle. We can determine the properties of the circle by comparing the equation to the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Comparing the equation (x+3)² + y² = 81 to the standard form, we can conclude the following:

1. The center of the circle would lie on the x-axis. The value of h is -3, which means the center of the circle is located at (-3, 0) on the x-axis.
2. The radius is 9. We can determine this by taking the square root of 81, which is the value of r in the standard form of the equation.

In summary, the correct answers are a) The center of the circle would lie on the x-axis and d) The radius is 9.