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Question

Question: The area of the rhombus enclosed by the lines ax ± by ± c = 0 is...

The area of the rhombus enclosed by the lines ax ± by ± c = 0 is

A

2c2/ab

B

2ab/c2

C

2c/ab

D

None of these

Answer

2c2/ab

Explanation

Solution

The four sides of the rhombus are

ax + by + c = 0, ax + by –c = 0, ax –by + c = 0,

ax – by – c = 0 .

On solving these equations, we get the vertices as A (c/a, 0),

B (0, c/b), C(-c/a, 0) and D(0, -c/b).

The length of the diagonal AC is 2c/a and that of the diagonal BD is 2c/b.

Theref ore the area of the rhombus is