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Write the equation in standard form for the ellipse 3x2+y2=243x^2 + y^2 = 24.

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Full solution

Q. Write the equation in standard form for the ellipse 3x2+y2=243x^2 + y^2 = 24.
  1. Simplify Fractions: Simplify the fractions.\newlineCalculation: x28+y224=1\frac{x^2}{8} + \frac{y^2}{24} = 1
  2. Check Standard Form: Check if the equation is in standard form.\newlineThe standard form for an ellipse is (x2a2)+(y2b2)=1(\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) = 1, where aa and bb are the lengths of the semi-major and semi-minor axes, respectively.\newlineOur equation matches this form, so we're done.

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