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

conic section is an ellipse
a^2 = 49
b^2 = 25
c^2 = a^2 - b^2 = 49-25 = 24 ---> c = sqrt(24) = 2sqrt(6)

center of ellipse is (-2,1)

foci points are "c" distance away from center along major axis
major axis is in the x direction because a^2 is under the "x" term

therefore coordinates are:
\[(-2 \pm 2\sqrt{6} , 1)\]

Answer 2

Thank you so much!

Answer 3

yw