What conic section does the equation $2 x^{2} + 4 x y + 6 y^{2} + 6 x + 2 y = 6$ $2x^2+4xy+6y^2+6x+2y=6$ represent?

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Answer 1 · 2014-09-28T19:26:32

First locate the coefficients for the $x^{2}$ $x^2$ term, $A$ $A$ , and the $y^{2}$ $y^2$ term, $C$ $C$ .

$A = 2$ $A=2$
$C = 6$ $C=6$

Characteristics of an ellipse.

$A \cdot C > 0$ $A*C>0$
$A \neq C$ $A!=C$

$2 \cdot 6 > 0$ $2*6>0$ True
$2 \neq 6$ $2!=6$ True

This is an ellipse .

What conic section does the equation 2x^2+4xy+6y^2+6x+2y=62x2+4xy+6y2+6x+2y=62x^2+4xy+6y^2+6x+2y=6 represent?