If a, c, b are in G.P then the line ax + by + c = 0

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has fixed direction

always passes through a fixed point

forms a triangle with the axes whose area is constant

always cuts intercepts on the axes such that their sum is zero

answer is C.

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Detailed Solution

If a, c, b are in GP

$\begin{array}{l} \Rightarrow c^{2} = a b \Rightarrow c = \pm \sqrt{a b} \\ G i v e n l i n e a x + b y + c = 0 \Rightarrow a x + b y \pm \sqrt{a b} = 0 \\ A r e a o f Δ^{l e} w i t h a x e s = \frac{c^{2}}{2 |a b|} \Rightarrow \frac{a b}{2 |a b|} \Rightarrow \frac{1}{2} i s c o n s \tan t \end{array}$

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