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Write the equation in standard form for the ellipse x2+8y2=16x^2 + 8y^2 = 16.

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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+8y2=16x^2 + 8y^2 = 16.
  1. Identify Standard Form: To write the equation of an ellipse in standard form, we need to have it 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 1616: Divide both sides of the equation x2+8y2=16x^2 + 8y^2 = 16 by 1616 to get the equation in standard form.\newlinex2/16+8y2/16=16/16x^2/16 + 8y^2/16 = 16/16
  3. Simplify Equation: Simplify the equation to get the standard form. x2/16+y2/2=1x^2/16 + y^2/2 = 1

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