Sketch the circle graph of (x + 2 )^2 + y^2 =9 ?

To sketch the circle graph of the equation (x + 2)^2 + y^2 = 9, we first need to rewrite the equation in standard form for a circle:

(x + 2)^2 + y^2 = 9
x^2 + 4x + 4 + y^2 = 9
x^2 + 4x + y^2 = 5

Now we can see that the center of the circle is at (-2, 0) and the radius is √5.

To sketch the circle, we can plot the center at (-2, 0) and then draw a circle with radius √5 around the center.

The circle graph of the equation (x + 2)^2 + y^2 = 9 will look like a circle centered at (-2, 0) with a radius of √5.

The equation (x^2)^2 y^2 = 9 can be rewritten as x^4 y^2 = 9. This equation represents a quartic curve, which is a curve of degree 4. To sketch the curve, we can use the following steps:

1. Factor the equation as follows:

x^4 y^2 = 9
x^2 y^2 = 3
xy = ±√3

2. The equation xy = √3 represents a hyperbola with vertices at (0, ±√3) and asymptotes y = ±√3x.

3. The equation xy = -√3 represents a hyperbola with vertices at (0, -√3) and asymptotes y = -√3x.

4. The two hyperbolas intersect at the origin (0, 0).

5. The circle graph of the equation (x^2)^2 y^2 = 9 consists of the two hyperbolas and the origin.

Here is a sketch of the circle graph:

[Image of the circle graph of the equation (x^2)^2 y^2 = 9]