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Write the equation in standard form for the ellipse with center at the origin, vertex $(-9,0)$ , 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

(-9,0)

, and co-vertex

(0,3)

.

Identify Vertex Value: Identify the value of $a$ using the vertex. $\newline$ Vertex: $(-9, 0)$ $\newline$ $a =$ distance from center to vertex $\newline$ $a = \sqrt{((-9 - 0)^2 + (0 - 0)^2)}$ $\newline$ $a = \sqrt{81}$ $\newline$ $a = 9$
Identify Co-vertex Value: Identify the value of $b$ using the co-vertex. $\newline$ Co-vertex: $(0, 3)$ $\newline$ $b =$ distance from center to co-vertex $\newline$ $b = \sqrt{(0 - 0)^2 + (3 - 0)^2}$ $\newline$ $b = \sqrt{9}$ $\newline$ $b = 3$
Write Standard Form Equation: Write the standard form equation of the ellipse. $\newline$ Center: $(0, 0)$ $\newline$ $a = 9$ , $b = 3$ $\newline$ Standard form: $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$ $\newline$ Plug in $h = 0$ , $k = 0$ , $a = 9$ , and $b = 3$ : $\newline$ $\frac{(x - 0)^2}{9^2} + \frac{(y - 0)^2}{3^2} = 1$ $\newline$ $x^2/81 + y^2/9 = 1$

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