Question

Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)

Answer 1

General equation of an ellipse:

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

where (h,k) is the center, and a and b are some constants.

If b² is greater than a², then the y-axis is the major axis.

In this case, the ellipse is defined by the next equation:

`((x-2)^2)/(4)+((y+5)^2)/(9)=1`

This means that:

`\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}`

And, h = 2, k = -5

The vertices on the major axis are computed as follows:

(h, k+b) and (h, k-b)

Substituting with h = 2, k = -5, and b = 3, the vertices are:

(2, -5+3) and (2, -5-3)

(2, -2) and (2, -8)