Problem 47
Question
Use a graphing utility to graph each equation. $$3 x^{2}+4 x y+6 y^{2}-7=0$$
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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 \(y = -\frac{3x^2 + 7}{4x + 6y}\).
2Step 2: 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.
3Step 3: 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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