Straight Line Question 343

Question: A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is [EAMCET 1994]

Options:

A) $ x+2y=5 $

B) $ x-y+1=0 $

C) $ x+y-3=0 $

D) $ 2x+y-4=0 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let the equation of the line be $ \frac{x}{a}+\frac{y}{b}=1 $ . The coordinates of the mid point of the intercept AB between the axes are $ ( \frac{a}{2},\frac{b}{2} ) $ . \ $ \frac{a}{2}=1,\frac{b}{2}=2\Rightarrow a=2,b=4 $ .Hence the equation of the line is $ \frac{x}{2}+\frac{y}{4}=1 $ , $ 2x+y=4 $ .

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