7. If ab > 0, find the area of the rhombus enclosed by the four straight lines ax+-by+-c=0
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In the question it is given the equation of a rhombus and is asking its area.
The four sides of the rhombus are,
ax + by + c = 0
ax + by - c = 1
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)
D(0, - c / b)
The length of the diagonal AC is 2c/a and that of the diagonal BD is 2c/b.
Therefore the area of the rhombus is,
1/2(2c/a)(2c/b)=2c²/ab
Therefore,
2c²/ab is the correct answer
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