SATHEE: Straight Line Question 380

Straight Line Question 380

Question: If a, b, c are in harmonic progression, then straight line $ \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0 $ always passes through a fixed point, that point is [MP PET 1999; AIEEE 2005]

Options:

A) $ (-1,\ -2) $

B) $ (-1,\ 2) $

C) $ (1,\ -2) $

D) $ (1,\ -1/2) $

Show Answer

Answer:

Correct Answer: C

Solution:

a, b, c are in H. P., then $ \frac{2}{b}=\frac{1}{a}+\frac{1}{c} $ …..(i) Given line is $ \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0 $ …..(ii) Subtracting both $ \frac{1}{a}(x-1)+\frac{1}{b}(y+2)=0 $ Since $ a\ne 0,b\ne 0 $ So, $ (x-1)=0\Rightarrow x=1\text{ and }(y+2)=0\Rightarrow y=-2 $ .Trick: Checking from options, let $ a,b,c $ are $ \frac{1}{1},\frac{1}{2},\frac{1}{3} $ . Then $ x+2y+3=0 $ will satisfy (c) option.

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Straight Line Question 380

Question: If a, b, c are in harmonic progression, then straight line $ \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0 $ always passes through a fixed point, that point is [MP PET 1999; AIEEE 2005]

Options:

Answer:

Solution:

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