Question

The locus of foot of the perpendicular drawn from a fixed point $(a,b)$ to the variable line $y=mx,m$ being variable is

• A. $x^2+y^2-ax+$ by $=0$
• B. $x+y-(a+b)=0$
• C. $x^2+y^2-ax-by=0$
• D. $xy-bx-ay+ab=0$

Answer 1

The correct option is C $x^2+y^2-ax-by=0$

$k=hm$

$m=\frac{k}{h}$

$\frac{k}{h}\times \left(\frac{b-k}{a-h}\right)=-1$

$h^2+k^2-ah-bk=0$

$x^2+y^2-ax-by=0$