Question

What is the length of the major axis of the ellipse (x-7)^2/4+(y+3)^2/16=1

Answer 1

$\bf \begin{array}{llll} \cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1\\\\ \cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1 \end{array}\quad \begin{cases} \textit{major axis}=a+a\\ a=\textit{the larger denominator}\\ b=\textit{smaller denominator} \end{cases}\\\\ -----------------------------\\\\ \cfrac{(x-7)^2}{4}+\cfrac{(y+3)^2}{16}=1\implies \cfrac{(x-7)^2}{2^2}+\cfrac{(y+3)^2}{4^2}=1\quad \begin{cases} a=4\\ b=2 \end{cases}$