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Write the equation in standard form for the ellipse 3x2+y2+6y−9=03x^2 + y^2 + 6y - 9 = 0.

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Full solution

Q. Write the equation in standard form for the ellipse 3x2+y2+6y−9=03x^2 + y^2 + 6y - 9 = 0.
  1. Complete the square for yy: Now, we complete the square for the yy terms.\newlineAdd (62)2=9\left(\frac{6}{2}\right)^2 = 9 to both sides to complete the square for yy.\newline3x2+y2+6y+9=9+93x^2 + y^2 + 6y + 9 = 9 + 9
  2. Simplify the equation: Simplify the equation. 3x2+(y+3)2=183x^2 + (y + 3)^2 = 18
  3. Divide by 1818: Divide everything by 1818 to get the standard form of the ellipse. x26\frac{x^2}{6} + (y+3)218\frac{(y + 3)^2}{18} = 11

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