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:

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

You can identify that it has this form:

`((x-h)^2)/(a^2)+((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=√(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=√(49-25)=2√(6)`

Notice that, in this case:

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

Therefore, the coordinates of the Foci are:

`(-2\pm2√(6),1)`

Hence, the answer is: Option B.