Given the following conic section, determine its shape and then sketch its graph. displaystyle{x}^{2}-{2}{x}{y}+{y}^{2}+{x}-{2}{y}-{1}={0}

Suman Cole 2021-02-22 Answered
Given the following conic section, determine its shape and then sketch its graph.
x22xy+y2+x2y1=0
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Expert Answer

lamusesamuset
Answered 2021-02-23 Author has 93 answers

Step 1
We need to determine the shape of the given conic section using its equation.
x22xy+y2+x2y1=0
Step 2
We know that, for the general equation of conic section
Ax2+Bxy+Cy2+Dx+Ey+F=0
if B24AC=0, then the conic must be a parabola.
For the given equation, A=1,B=2,C=1
B24AC=(2)24(1)(1)
=0=> given conic section is a parabola
Step 3
The graph of the parabola has been shown below.
image

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