Question

Which of the following expresses the coordinates of the foci of the conic section shown below?(x + 2)² /49+ (y − 1)²/25 = 1

Answer 1

Given the conic section:

$\frac{(x+2)^2}{49}+\frac{(y-1)^2}{25}=1$

You can identify that it has this form:

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

That is the form of the Equation of an Ellipse.

By definition, the coordinates of the foci of an ellipse are:

$(h\pm c,k)$

Where:

$c=\sqrt{a^2-b^2}$

In this case, you can identify that:

$\begin{gathered} a^2=49 \\ b^2=25 \end{gathered}$

Therefore, you can find "c":

$c=\sqrt{49-25}=2\sqrt{6}$

Notice that, in this case:

$\begin{gathered} h=-2 \\ k=1 \end{gathered}$

Therefore, the coordinates of the Foci are:

$(-2\pm2\sqrt{6},1)$

Hence, the answer is: Option B.