QJEEM05Maa5d5: JEE Main 2005 Mathematics - Class 11 JEEM05Maa5d5 Solution: If non zero numbers a , b , c are in H . P . , then the…

Question

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If non zero numbers

a, b, c

are in

H . P .,

then the straight line

\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0

always passes through a fixed point. That point is :

Accepted Answer

a, b, c

are in

H . P . \Rightarrow \frac{1}{a} . \frac{1}{b}, \frac{1}{c}

are in

A . P .

\Rightarrow \frac{2}{b} = \frac{1}{a} + \frac{1}{c}

\Rightarrow \frac{1}{a} - \frac{2}{b} + \frac{1}{c} = 0

∴

\frac{x}{a} + \frac{y}{a} + \frac{1}{c} = 0

passes through

(1, - 2)

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