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Q51.

Expert-verifiedFound in: Page 677

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.

$3{x}^{2}-2xy+{y}^{2}+4x+2y-1=0$The equation defines ellipse.

The given equation is $3{x}^{2}-2xy+{y}^{2}+4x+2y-1=0$

Here $A=3,B=-2,C=1$

${B}^{2}-4AC={\left(-2\right)}^{2}-4\left(3\right)\left(1\right)\phantom{\rule{0ex}{0ex}}{B}^{2}-4AC=4-12=-8<0$

The equation defines ellipse.

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