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Write the equation in standard form for the ellipse with vertices $(-11,0)$ and $(11,0)$ , and co-vertices $(0,2)$ and $(0,-2)$ .

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Write equations of ellipses in standard form using properties

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Q. Write the equation in standard form for the ellipse with vertices

(-11,0)

and

(11,0)

, and co-vertices

(0,2)

and

(0,-2)

.

Calculate semi-major axis: Vertices are $(-11, 0)$ and $(11, 0)$ , so the major axis is horizontal and the length of the major axis is $2a$ , where $a$ is the semi-major axis. $\newline$ Calculate $a$ : $a = 11$ (since the vertex is $11$ units away from the center at the origin).
Calculate semi-minor axis: Co-vertices are $(0, 2)$ and $(0, -2)$ , so the minor axis is vertical and the length of the minor axis is $2b$ , where $b$ is the semi-minor axis. $\newline$ Calculate $b$ : $b = 2$ (since the co-vertex is $2$ units away from the center at the origin).
Standard form equation: The standard form of the equation for an ellipse with a horizontal major axis is $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$ , where $(h, k)$ is the center of the ellipse. $\newline$ Since the center is at the origin, $h = 0$ and $k = 0$ .
Plug in values and simplify: Plug in the values of $a$ and $b$ into the standard form equation. $\newline$ Equation: $\frac{(x-0)^2}{11^2} + \frac{(y-0)^2}{2^2} = 1$ $\newline$ Simplify the equation: $\frac{x^2}{121} + \frac{y^2}{4} = 1$

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