EdelY654518 EdelY654518
  • 03-11-2022
  • Mathematics
contestada

Complete the square to rewrite the equation into standard form, show all work please x^2+6x+y^2-4y=-9

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SofiC239658 SofiC239658
  • 03-11-2022
[tex](x+3)^{2}+(y-2)^{2}=4[/tex]

1) The first step is to divide the coefficient b by 2

[tex]\begin{gathered} b=6\therefore\frac{6}{2}=3 \\ b=-\frac{4}{2}\therefore=-\frac{4}{2}=-2 \end{gathered}[/tex]

2) So now, let's add to both sides those squared numbers to both sides of the equation and then write them as binomials:

[tex]\begin{gathered} x^2+6x+3^2+y^2-4x+(-2)^2=-9+9+4 \\ (x+3)^2+(y-2)^2=4 \end{gathered}[/tex]

Note that this is the Equation of the Circle in its standard form, whose radius is 4

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