Question

9 write an equation in standard form of an ellipse that has a vertex at (-6, 0), a co - vertex at (0, 5), and a center at the origin. options: \\(\frac{x^2}{25}+\frac{y^2}{-36}=1\\), \\(\frac{x^2}{25}+\frac{y^2}{36}=1\\), \\(\frac{x^2}{36}+\frac{y^2}{25}=1\\), \\(\frac{x^2}{5}+\frac{y^2}{6}=1\\)

Explanation:

Step1: Identificar parámetros del elipse

Centro en $(0,0)$, vértice en $(-6,0)$ → $a=6$, semi-eje menor $b=5$

Step2: Usar fórmula estándar del elipse

Fórmula para elipse horizontal: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Step3: Sustituir valores de $a$ y $b$

$a^2=6^2=36$, $b^2=5^2=25$ → $\frac{x^2}{36}+\frac{y^2}{25}=1$

Answer:

$\boldsymbol{\frac{x^2}{36}+\frac{y^2}{25}=1}$