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Write the equation in standard form for the ellipse 7x2+y2=217x^2 + y^2 = 21.\newline______

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Q. Write the equation in standard form for the ellipse 7x2+y2=217x^2 + y^2 = 21.\newline______
  1. Identify equation and goal: Identify the given equation and the goal.\newlineThe given equation is 7x2+y2=217x^2 + y^2 = 21, and we need to write it in standard form for an ellipse.
  2. Recognize standard form: Recognize the standard form of an ellipse.\newlineThe standard form of 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.
  3. Divide equation by 2121: Divide the given equation by 2121 to transform it into standard form.\newline(7x2)/21+(y2)/21=21/21(7x^2)/21 + (y^2)/21 = 21/21\newlineSimplify the equation:\newline(x2/3)+(y2/21)=1(x^2/3) + (y^2/21) = 1
  4. Verify equation in standard form: Verify that the equation is now in standard form.\newlineThe equation (x23)+(y221)=1(\frac{x^2}{3}) + (\frac{y^2}{21}) = 1 is in the standard form of an ellipse, where a2=3a^2 = 3 and b2=21b^2 = 21.

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