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Write the equation in standard form for the ellipse 5x2+y2=255x^2 + y^2 = 25.

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Full solution

Q. Write the equation in standard form for the ellipse 5x2+y2=255x^2 + y^2 = 25.
  1. Divide by 2525: Divide both sides of the equation by 2525 to get the standard form. \newline5x225+y225=2525\frac{5x^2}{25} + \frac{y^2}{25} = \frac{25}{25}
  2. Simplify fractions: Simplify the fractions. x25+y225=1\frac{x^2}{5} + \frac{y^2}{25} = 1
  3. Check standard form: Check if the equation is in standard form for an ellipse.\newlineThe standard form for an ellipse is (x2/a2)+(y2/b2)=1(x^2/a^2) + (y^2/b^2) = 1, where aa and bb are the lengths of the semi-major and semi-minor axes, respectively.

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