Answer :

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


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