Question

What is the length of the major axis of the conic section shown below?(x − 2)² /4 + (y+ 5)² /9 = 1

Answer 1

Solution:

Given the standard form of equation of ellipse:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

Relating it to the equation given as;

$\begin{gathered} \frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1 \\ \\ \frac{(x-2)^2}{2^2}+\frac{(y+5)^2}{3^2}=1 \end{gathered}$

The length of the major axis is 2a.

Thus, the length of the major axis of the ellipse is;

$\begin{gathered} a=2; \\ \\ L=2a \\ \\ L=2(2) \\ \\ L=4units \end{gathered}$