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}

Question
Conic sections
asked 2021-02-22
Given the following conic section, determine its shape and then sketch its graph.
\(\displaystyle{x}^{2}-{2}{x}{y}+{y}^{2}+{x}-{2}{y}-{1}={0}\)

Answers (1)

2021-02-23
Step 1
We need to determine the shape of the given conic section using its equation.
\(\displaystyle{x}^{2}-{2}{x}{y}+{y}^{2}+{x}-{2}{y}-{1}={0}\)
Step 2
We know that, for the general equation of conic section
\(\displaystyle{A}{x}^{2}+{B}{x}{y}+{C}{y}^{2}+{D}{x}+{E}{y}+{F}={0}\)
if \(\displaystyle{B}^{2}-{4}{A}{C}={0},\) then the conic must be a parabola.
For the given equation, \(\displaystyle{A}={1},{B}=-{2},{C}={1}\)
\(\displaystyle{B}^{2}-{4}{A}{C}={\left(-{2}\right)}^{2}-{4}{\left({1}\right)}{\left({1}\right)}\)
\(\displaystyle={0}=>\) given conic section is a parabola
Step 3
The graph of the parabola has been shown below.
image
0

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