Question

The equation of a straight line upon which the length of the perpendicular from the origin is $5$ and slope of this perpendicular is $ 3/4 $ is

• A. $ 2x+5y\pm 16=0 $
• B. $ 4x+3y\pm 25=0 $
• C. $ 4x+3y\pm 5=0 $
• D. $ 2x+5y\pm 4=0 $

Answer 1

Answer: (B)

Let $ y=mx+c $ be the equation of straight line
$ \Rightarrow $ $ mx-y+c=0 $ ..(i)
Now, by condition Perpendicular distance from origin to line (i) = 5
$ \Rightarrow $ $ \frac{|0-0+c|}{\sqrt{{{m}^{2}}+1}}=5 $
$ \Rightarrow $ $ c=\pm 5\sqrt{{{m}^{2}}\pm 1} $ ..(ii)
Also, given that Slope of perpendicular to line (i) from the origin
$ =\frac{3}{4} $
$ \Rightarrow $ $ -\frac{1}{m}=\frac{3}{4} $
$ \Rightarrow $ $ m=\frac{-4}{3} $
From Eq. (ii), $ c=\pm 5\sqrt{{{m}^{2}}+1} $
$ c=\pm 5\sqrt{1+\frac{16}{9}}=\pm 5\times \frac{5}{3}=\pm \frac{25}{3} $
On putting the values of m and c in Eq. (i), we get
$ -\frac{4x}{3}-y\pm \frac{25}{3}=0 $
$ \Rightarrow $ $ 4x+3y\pm 25=0 $
which is required equation of straight line.