Answer
(a)
Center: $C(3,0)$
$V_1(3,-4)$ and $V_2(3,4)$
$F_1(3,-\sqrt 7)$ and $F_2(3,\sqrt 7)$
(b)
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=6$
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is vertical):
$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
$\frac{(x-3)^2}{9}+\frac{y^2}{16}=1$
$\frac{(x-3)^2}{3^2}+\frac{(y-0)^2}{4^2}=1$
$h=3$
$k=0$
Center: $C(3,0)$
$a=4$
$b=3$
$c^2=a^2-b^2=16-9=7$
$c=\sqrt 7$
The given equation can be obtained by shifting
$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$
right 3 units. In this equation:
Vertices: $V(0,±a)$
$V_1(0,-4)$ and $V_2(0,4)$
Foci: $F(0,±c)$
$F_1(0,-\sqrt 7)$ and $F_2(0,\sqrt 7)$
Now, shift these points 3 units:
$V_1(3,-4)$ and $V_2(3,4)$
$F_1(3,-\sqrt 7)$ and $F_2(3,\sqrt 7)$
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=6$
