Problem 52
Question
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed \(2 x^{2}-3 y^{2}+6 y+4=0\) by using the procedure for writing the equation of a rotated conic in standard form.
Step-by-Step Solution
Verified Answer
The statement does not make sense because the equation \(2 x^{2}-3 y^{2}+6 y+4=0\) doesn't represent a rotated conic. Thus, using a procedure for rotating a conic to graph it is incorrect.
1Step 1: Identify the Given Equation
The first step is to inspect the equation \(2 x^{2}-3 y^{2}+6 y+4=0\). The variables are not mixed (i.e. there's no term like x*y), therefore it doesn't appear to be a rotated conic. Instead, the equation appears to be in a general form of a conic which can represent an ellipse, parabola or hyperbola, but not a rotated one.
2Step 2: Assess the Statement
Since the given equation doesn't appear to be a rotated conic, trying to graph it using the procedure for rotating a conic wouldn't make sense. Consequently, the statement doesn't make sense because the wrong procedure was used to graph the equation.
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