Question

What is the length of the major axis of the conic section shown below? (x=33-404212 - = ) + (+2) = 1 49 25 O A. 5 OB. 10 C. O c. 7 O D. 14

Answer 1

Given:

`((x-3)^2)/(25)+((y+2)^2)/(49)=1`

Let's find the length of the major axis of the given conic section.

Apply the equation of an ellipse:

`(x^2)/(a^2)+(y^2)/(b^2)=1`

Where b is greater than a.

The length of the major axis is = 2b

We have:

`\begin{gathered} a=\sqrt[]{25}=5 \\ \\ b=\sqrt[]{49}=7 \end{gathered}`

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