Question

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

• A. $(0,-\frac{1}{a})$
• B. $(0,\frac{a}{m})$
• C. $(0,-\frac{a}{m})$
• D. $(0,\frac{1}{a})$

Answer 1

Answer: (B)

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

Let $(h,k)$ be the required point.

$\frac{h-p}{a}=\frac{k-q}{b}=\frac{-(a\times p+b\times q+c)}{a^2+b^2}$

$\frac{h-a}{m^2}=\frac{k-0}{-m}=-\frac{(m^{2}a+a)}{m^4+m^2}$
$\Rightarrow \frac{h-a}{m^2}=\frac{k}{-m}=-\frac{a}{m^2}$
$\Rightarrow h=0,k=\frac{a}{m}$
Hence, the required point is $(0,\frac{a}{m})$