Identify the equation without applying a rotation of axes. displaystyle{4}{x}^{2}-{8}{x}{y}+{4}{y}^{2}-{3}{x}+{6}={0}

Brittney Lord 2021-02-25 Answered
Identify the equation without applying a rotation of axes.
4x28xy+4y23x+6=0
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Expert Answer

sovienesY
Answered 2021-02-26 Author has 89 answers

Step 1
Consider the provided equation:
4x28xy+4y23x+6=0
Step 2
Now, compare this equation with the general form of conic section:
Ax2+Bxy+Cy2+Dx+Ey+F=0
Step 3
Now, it is known that:
If B24AC<0, then it will be either circle or an ellipse.
If B24AC=0, then it will be a parabola.
If B24AC>0, then it will be a hyperbola.
Now, here we have, A=4,B=8andC=4
So, B24AC=(8)24(4)(4)=6464=0
Since, B24AC=0
Hence, the provided equation represents a parabola if a conic section exists.

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