Given:
[tex]\frac{(x-3)^2}{25}+\frac{(y+2)^2}{49}=1[/tex]
Let's find the length of the major axis of the given conic section.
Apply the equation of an ellipse:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where b is greater than a.
The length of the major axis is = 2b
We have:
[tex]\begin{gathered} a=\sqrt[]{25}=5 \\ \\ b=\sqrt[]{49}=7 \end{gathered}[/tex]
Here, b is greater than a.
Therefore, the length of the major axis is = 2b.
Where:
b = 7
Length of major axis = 2b = 2(7) = 14
Therefore, the length of the major axis is 14.
ANSWER:
D. 14
