Question: A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through [IIT 1977]
Options:
A)A fixed point
B)A variable point
C)Origin
D)None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Take two perpendicular lines as the coordinate axes. If a, b be the intercepts made by the moving line on the coordinate axes, then the equation of the line is $ \frac{x}{a}+\frac{y}{b}=1 $…..(i) According to the question $ \frac{1}{a}+\frac{1}{b}=\frac{1}{k} $ , (say) i.e., $ \frac{k}{a}+\frac{k}{b}=1 $ …..(ii) The result (ii) shows that the straight line (i) passes through a fixed point (k, k).
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