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Write the equation in standard form for the ellipse x2+2y2=12x^2 + 2y^2 = 12.

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Full solution

Q. Write the equation in standard form for the ellipse x2+2y2=12x^2 + 2y^2 = 12.
  1. Simplify fractions: Now simplify the fractions.\newlineCalculation: x212+y26=1\frac{x^2}{12} + \frac{y^2}{6} = 1
  2. Standard form check: Check if it looks like the standard form of an ellipse equation.\newlineStandard form check: (x2a2)+(y2b2)=1(\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) = 1, where a2a^2 and b2b^2 are the denominators.

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