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Write the equation in standard form for the ellipse $x^2 + 9y^2 - 2x - 26 = 0$ .

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Convert equations of ellipses from general to standard form

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Q. Write the equation in standard form for the ellipse

x^2 + 9y^2 - 2x - 26 = 0

.

Complete the Square for $x$ : Now, we complete the square for the $x$ terms. To do this, we take half of the coefficient of $x$ , which is $-1$ , square it, and add it to both sides. $\newline$ $x^2 - 2x + 1^2 + 9y^2 = 26 + 1$ $\newline$ $x^2 - 2x + 1 + 9y^2 = 27$
Rewrite Equation for x: We don't need to complete the square for the $y$ terms because there is no linear $y$ term. Now, we can rewrite the equation to show the perfect square trinomial for $x$ . $(x - 1)^2 + 9y^2 = 27$
Divide by $27$ : Next, we divide the entire equation by $27$ to get the standard form of the ellipse equation. $\newline$ $(x - 1)^2/27 + 9y^2/27 = 27/27$
Simplify the Equation: Simplify the equation by reducing the fractions. $\frac{(x - 1)^2}{27} + \frac{y^2}{3} = 1$

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