Question

Which of the following expresses the coordinates of the foci of the conic section shown below? 2 2 (x + 2), (-1)? + 1 64 81 ( - -24 145,1) В. o O A. OB. (-2,17717) Oc(-2,1V145) OC. Od (-2+V17,1)

Answer 1

The equation of a vertical ellipse is given by:

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

where (h,k) is its center. For the ellipse given the center is (-2,1), a squared is 81 and b squared is 64.

Now we know that the foci of the ellipse are a distance c of the center, where:

`\begin{gathered} c^2=a^2-b^2 \\ \end{gathered}`

Plugging the values and solving for c we have:

`\begin{gathered} c^2=81-64 \\ c^2=17 \\ c=\sqrt[]{17} \end{gathered}`

Finally, since this is a vertical ellipse we have to add and substract c to the y component of the center, therefore the foci are:

`(-2,1\pm\sqrt[]{17})`

and the answer is B.