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Write the equation in standard form for the ellipse 4x2+y2=164x^2 + y^2 = 16.

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Full solution

Q. Write the equation in standard form for the ellipse 4x2+y2=164x^2 + y^2 = 16.
  1. Divide by 1616: Divide both sides of the equation by 1616 to get the standard form.4x216+y216=1616\frac{4x^2}{16} + \frac{y^2}{16} = \frac{16}{16}
  2. Simplify fractions: Simplify the fractions. x24+y216=1\frac{x^2}{4} + \frac{y^2}{16} = 1
  3. Check standard form: Check the equation to ensure it's in standard form for an ellipse.\newlineThe standard form 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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