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Write the equation in standard form for the ellipse x2+2y2−16y+28=0x^2 + 2y^2 - 16y + 28 = 0.

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Convert equations of ellipses from general to standard formright chevron icon

Full solution

Q. Write the equation in standard form for the ellipse x2+2y2−16y+28=0x^2 + 2y^2 - 16y + 28 = 0.
  1. Complete the square for yy: Now, we complete the square for the yy terms. To do this, we add (82)2=16\left(\frac{8}{2}\right)^2 = 16 to both sides, inside the parenthesis for yy.x2+2(y2−8y+16)=−28+2(16)x^2 + 2(y^2 - 8y + 16) = -28 + 2(16)
  2. Simplify the equation: Simplify the equation by performing the addition. x2+2(y−4)2=4x^2 + 2(y - 4)^2 = 4
  3. Divide for standard form: Now, divide the whole equation by 44 to get the standard form of the ellipse.x24+(y−4)22=1\frac{x^2}{4} + \frac{(y - 4)^2}{2} = 1

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