Question

What are the coordinates of the foci of the conic section shown below?
(x+2)^2/16-(y-3)^2/9=1

Answer 1

a. (-2±5,3)
b. (-2,3±5)
c. (2,3±√7)
d. (-2±√7,3)

Answer 2

ok
here centre is at (-2,3)
here a=4
b=3
c^2=a^2+b^2
\[\Large c=\sqrt{a^2+b^2}=\sqrt{16+9}=\sqrt{25}=5\]
foci are (-c,0) and (+c,0)
or \[\Large (\pm C,0)=(\pm 5,0)\]
but center is at (-2,3)
so
\[\Large (-2 \pm 5,3)\]

option a is more appropriate !

Answer 3

did you get it ? @SantanaG

Answer 4

yeah thank you! :)