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Chapter 10: Problem 47

Use a graphing utility to graph each equation. $$3 x^{2}+4 x y+6 y^{2}-7=0$$

Short Answer

Expert verified
The graph of the equation \(3 x^{2}+4 x y+6 y^{2}-7=0\) can be obtained by firstly isolating y, then inserting this equation into a graphing utility and finally generating the graph. The graph gives a visual representation of solutions of the given equation.

Step by step solution

01

Isolate y-variable

For a graphing utility, it is better to have the equation in terms of one variable. In this case, it is easier to isolate y because dividing the whole equation by the coefficient of the x^{2} term could lead to decimals. Isolate y in the equation \(3 x^{2}+4 x y+6 y^{2}-7=0\) to obtain \(y = -\frac{3x^2 + 7}{4x + 6y}\).
02

Insert the equation into the graphing utility

Now, insert the above obtained equation into the graphing utility. Most graphing utilities have an input field where you can simply type in the equation.
03

Generate the graph

After inserting the equation into the graphing utility, generate the graph. The utility should provide a visual representation of the equation \(3 x^{2}+4 x y+6 y^{2}-7=0\).

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