Question

Write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9, -7

Answer 1

Recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.

so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.

$\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}\pm a, {{ k}}) \end{cases}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} a=\frac{30}{2}\\ b=\frac{14}{2}\\ h=-9\\ k=-7 \end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1 \\\\\\ \cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1$