Question
Question: The graph of y<sup>2</sup> + 2xy + 40 \|x\| = 400 divides the plane into regions. The area of the bo...
The graph of y2 + 2xy + 40 |x| = 400 divides the plane into regions. The area of the bounded region is-
A
400 sq. units
B
600 sq. units
C
800 sq. units.
D
1000 sq. units
Answer
800 sq. units.
Explanation
Solution
y2
= 2xy + 40|x| – 400 = 0 can be factorised as
(y + 20) (y + 2x – 20) = 0 for x ³ 0 and (y – 20) (y + 2x + 20) = 0 for x < 0
The bounded region is parallelogram of area 20 × 40 = 800 sq. units.