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Write the equation in standard form for the ellipse 3x2+y2+2y−26=03x^2 + y^2 + 2y - 26 = 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 3x2+y2+2y−26=03x^2 + y^2 + 2y - 26 = 0.
  1. Complete the square for yy terms: Now, we complete the square for the yy terms.\newlineTo do this, we add and subtract (22)2(\frac{2}{2})^2, which is 11, inside the parentheses.\newline3x2+(y2+2y+1−1)=263x^2 + (y^2 + 2y + 1 - 1) = 26
  2. Rewrite yy terms as perfect square: We can now rewrite the yy terms as a perfect square and simplify the equation.3x2+((y+1)2−1)=263x^2 + ((y + 1)^2 - 1) = 26
  3. Add 11 to isolate perfect square: Next, we add 11 to both sides to isolate the perfect square on the left side.\newline3x2+(y+1)2=273x^2 + (y + 1)^2 = 27
  4. Divide to get standard form: Now, we divide the entire equation by 2727 to get the standard form of the ellipse.x29\frac{x^2}{9} + (y+1)227\frac{(y + 1)^2}{27} = 11

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