58. Area of an ellipse The upper half of

Question

58. Area of an ellipse The upper half of the ellipse centered
at the origin with axes of length 2a and 2b is described by
b
y = V22 - x? (see figure). Find the area of the ellipse in
Va²
(
terms of a and b.
-
a
YA
y =
ba2-x²
b
=
a
)
-a
X
-b

Kunduz · Accepted Answer

(ob)
Coordinates of vertices of
ellipse are (a,0), (0.b),
{a,o) and ro-b)
(-a,o)
x
(a,0)
O
We will first find the area
of ellipse is first quadrant
१
:. Area of ellipse in Ist quadrant = Jyde
.
X=0
a
=j a
-S b vannede
[ Jaz nedir
j
rzo
9
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slo
wo
rei
Putra asio
dna acoso de
pt ned
0 20
nea
021/
7/2
Reqd area
= b
Svaraksiño, a los del
o
020
Tile
- Sino)
a wrodu
no
X
De
= blah) s Coso caso do
(
TIL
2 os?odo
Rab
2
1)
al s it
(It has 20 ) do
2
020

58. Area of an ellipse The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described by b y =