Straight Line Question 293

Question: The equation of the line perpendicular to the line $ \frac{x}{a}-\frac{y}{b}=1 $ and passing through the point at which it cuts x-axis, is [RPET 1996; Kerala (Engg.) 2002]

Options:

A) $ \frac{x}{a}+\frac{y}{b}+\frac{a}{b}=0 $

B) $ \frac{x}{b}+\frac{y}{a}=\frac{b}{a} $

C) $ \frac{x}{b}+\frac{y}{a}=0 $ $ $

D) $ \frac{x}{b}+\frac{y}{a}=\frac{a}{b} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • The given line is $ bx-ay=ab $ Obviously it cuts $ x $ -axis at (a, 0). The equation of line perpendicular to (i) is $ ax+by=k $ , but it passes through (a, 0)
    Þ $ k=a^{2} $ . Hence required equation of line is $ ax+by=a^{2} $ i.e., $ \frac{x}{b}+\frac{y}{a}=\frac{a}{b} $ .