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Write the equation in standard form for the ellipse x2+7y2=21x^2 + 7y^2 = 21.

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Convert equations of conic sections from general to standard formright chevron icon

Full solution

Q. Write the equation in standard form for the ellipse x2+7y2=21x^2 + 7y^2 = 21.
  1. Identify Standard Form: To write the equation in standard form, we need to have the equation in the form (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.
  2. Divide by 2121: Divide both sides of the equation x2+7y2=21x^2 + 7y^2 = 21 by 2121 to get the equation in standard form.\newline(x2/21)+(7y2/21)=21/21(x^2/21) + (7y^2/21) = 21/21
  3. Simplify Equation: Simplify the equation to get the standard form. x221+y23=1\frac{x^2}{21} + \frac{y^2}{3} = 1

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