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Consider the straight line a x+b y=c  where a, b, c \in R^{+} This line meets the coordinate axes at ‘P’ and ‘Q’ respectively. If the area of triangle OPQ, ‘O’ being origin, does not depend upon a, b and c,then

Option: 1

a, b, c are in G.P.


Option: 2

a, c, b are in G.P.


Option: 3

a, b, c are in A.P


Option: 4

a, c, b are inA.P.


Answers (1)

best_answer

\mathrm{P} \equiv\left(\frac{\mathrm{c}}{\mathrm{a}}, 0\right), \mathrm{Q} \equiv\left(0, \frac{\mathrm{c}}{\mathrm{b}}\right)
\Delta_{\mathrm{OPQ}}=\frac{1}{2}(\mathrm{OP})(\mathrm{OQ})
=\frac{1}{2} \frac{\mathrm{c}^2}{\mathrm{ab}} \text { clearly } \Delta_{\mathrm{OPQ}}  will not depend upon a, b and c if c^2=a b
i.e. a, c, b are in G.P

Posted by

Suraj Bhandari

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