Answer
(a)
Center: $C(2,-3)$
Vertices: $V(±5,0)$
Foci: $F(±3,0)$
(b)
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=8$
(c)
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is horizontal):
$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$
$\frac{(x-2)^2}{25}+\frac{(y+3)^2}{16}=1$
$\frac{(x-2)^2}{5^2}+\frac{[y-(-3)]^2}{4^2}=1$
$h=2$
$k=-3$
Center: $C(2,-3)$
$a=5$
$b=4$
$a^2=b^2+c^2$
$c^2=a^2-b^2=5^2-4^2=25-16=9$
$c=3$
Vertices: $V(±a,0)=V(±5,0)$
Foci: $F(±c,0)=F(±3,0)$
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=8$
