Question

The coordinates of the foot of perpendicular from $(a,0)$ on the line $y=mx+\frac{a}{m}$ are

• A. $(0,\frac{a}{m})$
• B. $(0,-\frac{a}{m})$
• C. $(\frac{a}{m},0)$
• D. $(-\frac{a}{m},0)$

Answer 1

Answer: (A)

$(0,\frac{a}{m})$

The equation of given line is
$y=mx+\frac{a}{m}$....(i)
The equation of line perpendicular to Eq. (i) is
$my+x+\lambda =0$....(ii)
The line passes through (a,0).
$\therefore 0+a+\lambda =0$
$\Rightarrow \lambda =-a$
On putting this value of $\lambda$ in Eq. (ii)
$my+x-a=0$....(iii)
On solving Eqs. (i) and (iii), we get
$x=0$ and $y=\frac{a}{m}$
$\therefore$ Coordinates of the foot of perpendicular are $(0,\frac{a}{m})$.