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Write the equation in standard form for the ellipse 6x2+y2=186x^2 + y^2 = 18.

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Full solution

Q. Write the equation in standard form for the ellipse 6x2+y2=186x^2 + y^2 = 18.
  1. Divide by 1818: We need to divide the equation by 1818 to get the standard form. \newline6x218+y218=1818\frac{6x^2}{18} + \frac{y^2}{18} = \frac{18}{18}
  2. Simplify fractions: Simplify the fractions. x23+y218=1\frac{x^2}{3} + \frac{y^2}{18} = 1
  3. Check standard form: Check if the equation looks like the standard form (x2/a2)+(y2/b2)=1(x^2/a^2) + (y^2/b^2) = 1.\newlineYep, it does.

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