First slide

Equation of line in Straight lines

Question

If the straight line $a x + b y + c = 0$ make a triangle of constant area with coordinate axes, then

Moderate

A

$a, b, c$ are in G.P.
B

$a, c, b$ are in G.P.
C

$c, a, b$ are in G.P.
D

none of these

Solution

Line $a x + b y + c = 0$ meets the coordinate axes at $A (- c / a, 0)$ and $(0, - c / b)$
$∴$ Area of $Δ O A B = \frac{1}{2} \times O A \times O B$
$\Rightarrow$ Area of $Δ O A B = \frac{1}{2} \times |- \frac{c}{a}| |- \frac{c}{b}| = c^{2}$
Clearly, this will be constant, if $a, c, b$ arc in $G . P .$

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