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Write the equation in standard form for the ellipse 6x2+y2+8y−8=06x^2 + y^2 + 8y - 8 = 0.

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Q. Write the equation in standard form for the ellipse 6x2+y2+8y−8=06x^2 + y^2 + 8y - 8 = 0.
  1. Complete the square: Now, we complete the square for the yy terms. To do this, we add (82)2=16\left(\frac{8}{2}\right)^2 = 16 to both sides of the equation.\newline6x2+y2+8y+16=8+166x^2 + y^2 + 8y + 16 = 8 + 16\newline6x2+(y+4)2=246x^2 + (y + 4)^2 = 24
  2. Divide by 2424: Next, we divide the entire equation by 2424 to get the standard form of the ellipse.\newline(x24)+((y+4)224)=1(\frac{x^2}{4}) + (\frac{(y + 4)^2}{24}) = 1\newlineOops, there's a mistake here. We forgot to divide the x2x^2 term by the correct number.

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