Area of rhombus bounded by four lines, ax pm by pm c = 0 is :

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9.Straight Line

normal

Area of the rhombus bounded by the four lines, $ax \pm by \pm c = 0$ is :

$\frac{{{c^2}}}{{2\,ab}}$

$\frac{{2\,{c^2}}}{{ab}}$

$\frac{{4\,{c^2}}}{{ab}}$

$\frac{{ab}}{{4\,{c^2}}}$

Solution

The four lines will form a rhombus. The coordinates of the vertices are $\left(-\frac{ c }{ a }, 0\right),\left(\frac{ c }{ a }, 0\right),\left(0, \frac{ c }{ b }\right),\left(0,-\frac{ c }{ b }\right)$

Let $d _1, d _2$ be the diagonals of the rhombus.

$d _1=\frac{2 c }{ a }$

$d _2=\frac{2 c }{ b }$

$\text { Area }=\frac{1}{2} d _1 \cdot d _2=\frac{2 c ^2}{ ab }$

Standard 11

Mathematics

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normal

Area of the rhombus bounded by the four lines, $ax \pm by \pm c = 0$ is :

Solution

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