Question

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a,b), is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\lambda (x-a)+(y-b)=0$ is the equation of line.

$r=-\left(\frac{-a\lambda -b}{{\lambda }^2+1}\right)$

Coordinates of point = $\{-\lambda \left(\frac{-a\lambda -b}{{\lambda }^2+1}\right),-\left(\frac{-a\lambda -b}{{\lambda }^2+1}\right)\}$

$h=\lambda \left(\frac{a\lambda +b}{{\lambda }^2+1}\right),k=\frac{a\lambda +b}{{\lambda }^2+1},\lambda =\frac{h}{k}$

$\therefore h=h\left(\frac{ah+kb}{h^2+k^2}\right)\Rightarrow x^2+y^2=ax+by$.