(a) Show that the parametric equations x = a sin u cos v , y = b sin u sin v , z = c cos u , 0 ≤ u ≤ π , 0 ≤ v ≤ 2 π , represent an ellipsoid. (b) Use the parametric equations in part (a) to graph the ellipsoid for the case a = 1 , b = 2 , c = 3 (c) Set up, but do not evaluate, a double integral for the surface area of the ellipsoid in part (b).
(a) Show that the parametric equations x = a sin u cos v , y = b sin u sin v , z = c cos u , 0 ≤ u ≤ π , 0 ≤ v ≤ 2 π , represent an ellipsoid. (b) Use the parametric equations in part (a) to graph the ellipsoid for the case a = 1 , b = 2 , c = 3 (c) Set up, but do not evaluate, a double integral for the surface area of the ellipsoid in part (b).
(a) Show that the parametric equations
x
=
a
sin
u
cos
v
,
y
=
b
sin
u
sin
v
,
z
=
c
cos
u
,
0
≤
u
≤
π
,
0
≤
v
≤
2
π
, represent an ellipsoid.
(b) Use the parametric equations in part (a) to graph the ellipsoid for the case
a
=
1
,
b
=
2
,
c
=
3
(c) Set up, but do not evaluate, a double integral for the surface area of the ellipsoid in part (b).
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