Answer
See graph
Foci: $(2,-4),(2,2)$
Work Step by Step
We are given the equation:
$\dfrac{(x-2)^2}{16}+\dfrac{(y+1)^2}{25}=1$
The standard form of the above equation is:
$\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1$:
Determine $h,k,a,b,c$:
$h=2$
$k=-1$
$a^2=25\Rightarrow a=\sqrt{25}=5$
$b^2=16\Rightarrow b=\sqrt{16}=4$
$c^2=a^2-b^2$
$c^2=25-16$
$c^2=9$
$c=\sqrt 9$
$c=3$
The center of the ellipse is:
$(h,k)=(2,-1)$
The endpoints of the major and minor axis are:
$(h,k-a)=(2,-1-5)=(2,-6)$
$(h,k+a)=(2,-1+5)=(2,4)$
$(h-b,k)=(2-4,-1)=(-2,-1)$
$(h+b,k)=(2+4,-1)=(6,-1)$
Use the center and the 4 endpoints to graph the ellipse.
Determine the foci:
$F_1(h,k-c)=(2,-1-3)=(2,-4)$
$F_2(h,k+c)=(2,-1+3)=(2,2)$
