Problem 48
Question
Use a graphing utility to graph each equation. $$3 x^{2}-6 x y+3 y^{2}+10 x-8 y-2=0$$
Step-by-Step Solution
Verified Answer
The graph of this equation is an ellipse. The exact parameters of the ellipse (center, axis lengths) depend on the specific graphing technology used.
1Step 1: Identify the general shape
Inspect the equation to identify its general shape. It is a second degree equation in both x and y. Since the coefficients of \(x^{2}\) and \(y^{2}\) are positive, it represents an ellipse.
2Step 2: Plug it into a Graphing Utility
The simplest way to graph this equation is to use a graphing utility. There are many options available, online as well as stand alone graphing calculators. Select the 'Graph' function, input the equation exactly as it appears, and execute the command.
3Step 3: Analyze the output
Explain the output from the graphing tool. Typically, the output will show an ellipse centered around some point in the plane. Depending on the system used, the center, axis lengths, or even orientation of the ellipse may be given or can be determined visually.
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