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Write the equation in standard form for the ellipse with center at the origin, vertex $(-10,0)$ , and co-vertex $(0,3)$ .

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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 center at the origin, vertex

(-10,0)

, and co-vertex

(0,3)

.

Identify Major Axis: Vertex is $(-10, 0)$ , so the major axis is horizontal and the length of the semi-major axis, $a$ , is $10$ . $\newline$ $a = 10$
Identify Co-vertex: Co-vertex is $(0, 3)$ , so the length of the semi-minor axis, $b$ , is $3$ . $\newline$ $b = 3$
Find Center: The center $(h, k)$ is at the origin, so $h = 0$ and $k = 0$ .
Standard Form Equation: The standard form for a horizontal ellipse is $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$ . Plug in $h = 0$ , $k = 0$ , $a = 10$ , and $b = 3$ . $(x-0)^2/10^2 + (y-0)^2/3^2 = 1$
Simplify Equation: Simplify the equation. $\frac{x^2}{100} + \frac{y^2}{9} = 1$

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