Question

Постройте график уравнения (x^2+y^2+6y)(x-y)=0

Answer 1

y=x y=-корень9-х^2-3 y=корень9-х^2-3

Answer 2

Graph of the Equation

To graph the equation \( (x^2+y^2+6y)(x-y)=0 \), we can start by analyzing the factors separately and then combine their graphs.

Factor 1: \(x^2+y^2+6y=0\)

The equation \(x^2+y^2+6y=0\) represents a circle in the xy-plane. Completing the square, we can rewrite it as \(x^2 + (y+3)^2 = 9\), which is the equation of a circle centered at (0, -3) with a radius of 3.

Factor 2: \(x-y=0\)

The equation \(x-y=0\) represents a straight line in the xy-plane. This line has a slope of 1 and passes through the origin.

Combined Graph

The graph of the combined equation \( (x^2+y^2+6y)(x-y)=0 \) is the union of the circle and the line. This means that the graph consists of the circle \(x^2 + (y+3)^2 = 9\) and the line \(x=y\).

By combining the graphs of the circle and the line, we can visualize the solution to the given equation.

Visualization

Unfortunately, I'm unable to generate the graph directly in this text-based format. However, you can use graphing software or online graphing tools to plot the circle and the line separately and observe their intersection points to understand the solution visually.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.