Identify the graph of the equation. What is the angle of rotation for the equation?

y^2+8x=0

is parabola 90 degrees correct?

also

Identify the graph of the equation. What is the angle of rotation for the equation?

xy = -5

=hyperbola 45 degrees

y^2+8x=0

is a parabola opening left

graph xy = -5
here,
http://fooplot.com/
put in y = -5/x
and click on plot it
You will see that the axis of symmetry is 45 degrees down and to the right of the x axis.

For the equation y^2 + 8x = 0, the graph is a parabola. The angle of rotation for this equation is 0 degrees since there is no rotation involved.

For the equation xy = -5, the graph is a hyperbola. However, the concept of angle of rotation is not applicable to hyperbolas. The angle of rotation is only relevant for conic sections that result from rotating a plane curve.

To identify the graph of an equation, you need to determine its shape by analyzing its form and coefficients. The angle of rotation refers to the angle by which the graph is rotated from its standard position.

1. Equation: y^2 + 8x = 0
This equation represents a parabola, but it is not rotated. The standard form of a parabola is x = Ay^2, where A is a constant. In the given equation, we can rewrite it as x = (-1/8)y^2. Since there is no angle of rotation mentioned or indicated in the equation, we can conclude that the angle of rotation for this equation is 0 degrees.

Therefore, the statement "parabola 90 degrees" is incorrect.

2. Equation: xy = -5
This equation represents a hyperbola, and to identify its angle of rotation, we need to determine its standard form. The standard form of a hyperbola is given by (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) represents the center, and a and b are constants.

To convert the given equation into the standard form, we divide both sides by -5, resulting in xy/-5 = 1. Rearranging, we get xy = 5, which can be written as (x-0)^2/5 - (y-0)^2/5 = 1.

In this standard form, we can see that there is no coefficient in front of the (y-k)^2 term. This indicates that the graph is not rotated at all. Therefore, the angle of rotation for this equation is 0 degrees.

Hence, the statement "hyperbola 45 degrees" is incorrect.