The equation x^2 - 2xy + y^2 + 3x + 2 = 0 rep | vedclass

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(A) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 - 2xy + y^2

Vedclass · Accepted Answer

$A$ parabola

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(A) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 - 2xy + y^2 + 3x + 2 = 0$,we have $a = 1$,$h = -1$,$b = 1$,$g = 3/2$,$f = 0$,and $c = 2$.First,we check the condition $h^2 - ab$:$h^2 - ab = (-1)^2 - (1)(1) = 1 - 1 = 0$.Since $h^2 - ab = 0$,the conic section represents a parabola (provided it is not a pair of parallel lines).To confirm it is not a degenerate conic,we check the determinant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2$:$\Delta = (1)(1)(2) + 2(0)(3/2)(-1) - (1)(0)^2 - (1)(3/2)^2 - (2)(-1)^2$$\Delta = 2 + 0 - 0 - 9/4 - 2 = -9/4 
eq 0$.Since $\Delta 
eq 0$ and $h^2 - ab = 0$,the equation represents a parabola.

The equation $x^2 - 2xy + y^2 + 3x + 2 = 0$ represents:

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