Write the area of the figure formed by the lines a|x| + b|y| + c = 0
Given:
a x + b y + c = 0; x, y ≥ 0 … (1)
-a x + b y + c = 0; x < 0 y ≥ 0 … (2)
-a x – b y + c = 0; x < 0 y < 0 … (3)
a x – b y + c = 0; x ≥ 0 y < 0 … (4)
To find:
The area of the figure formed by the lines a|x| + b|y| + c = 0
Explanation:
The given lines can be written separately in the following way:
a x + b y + c = 0; x, y ≥ 0 … (1)
-a x + b y + c = 0; x < 0 y ≥ 0 … (2)
-a x – b y + c = 0; x < 0 y < 0 … (3)
a x – b y + c = 0; x ≥ 0 y < 0 … (4)
The lines and the region enclosed between them is shown below.
So, the area of the figures formed by the lines a |x| + b |y| + c = 0 is
Square units