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Write the equation in standard form for the ellipse x2+6y2−18=0x^2 + 6y^2 - 18 = 0.

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Full solution

Q. Write the equation in standard form for the ellipse x2+6y2−18=0x^2 + 6y^2 - 18 = 0.
  1. Divide by 1818: Now, divide each term by 1818 to get the standard form of the ellipse. x218+6y218=1818\frac{x^2}{18} + \frac{6y^2}{18} = \frac{18}{18}
  2. Simplify the equation: Simplify the equation by reducing the fractions. x218+y23=1\frac{x^2}{18} + \frac{y^2}{3} = 1
  3. Fix previous mistake: Oops, I made a mistake in the previous step. I should have divided 6y26y^2 by 1818 correctly.\newlineLet's fix that.\newline(x2)/18+(6y2)/18=1(x^2)/18 + (6y^2)/18 = 1\newline(x2)/18+(y2)/3=1(x^2)/18 + (y^2)/3 = 1

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