Question

What is the length of the major axis of the conic section shown below?

Answer 1

$\dfrac{(x-2)^2}{49}+\dfrac{(y+5)^2}{36}=1$

The equation of a elipse:

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

The length of the major axis is equal 2a if a > b or 2b if b > a.

We have

$a^2=49\to a=\sqrt{49}=7\\\\b^2=36\to b=\sqrt{36}=6\\\\a > b$

therefore the length of the major axis is equal 2 · 7 = 14.