Solution Given equation of the ellipse 9x2 + y2 = 36 can be expressed as 
2
2
1
4
36
x
+y
=  or
2
2
2
2
1
2
6
x
+y
= and hence, its shape is as given in Fig 8 17 Accordingly, the equation of the chord AB is
y – 0 = 6
0 (
2)
0
−2 x
−
−
or
y = – 3(x – 2)
or
y = – 3x + 6
Area of the shaded region as shown in the Fig 8 17