Question

The equation of circle passing through the origin and cutting off equal intercepts of $4$ units on the lines $xy=0$ can be

• A. $x(x-4)+y(y-4)=0$
• B. $x(x+4)+y(y-4)=0$
• C. $x(x+4)+y(y+4)=0$
• D. $x(x-4)+y(y+4)=0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $x(x-4)+y(y-4)=0$
B $x(x+4)+y(y-4)=0$
C $x(x+4)+y(y+4)=0$
D $x(x-4)+y(y+4)=0$


Given : $xy=0$
$\Rightarrow x=0$ or $y=0$
Points on the line $y=0$ which is $4$ units from the origin :
$A\equiv (4,0)$ and $C\equiv (-4,0)$
Points on the line $x=0$ which is $4$ units from the origin :
$B\equiv (0,4)$ and $D\equiv (0,-4)$

Since both these lines are perpendicular,
so, using diametric form for equation of circle with :
$AB$ as diameter is $(x-4)(x-0)+(y-0)(y-4)=0,$
$BC$ as diameter is $(x-0)(x+4)+(y-4)(y-0)=0,$
$CD$ as diameter is $(x+4)(x-0)+(y-0)(y+4)=0,$
$AD$ as diameter is $(x-4)(x-0)+(y-0)(y+4)=0$