Question

Question

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.

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