Question

The line $\frac{x}{a}+\frac{y}{b}=1$ meets the $x$-axis and the $y$ axis $A$ and $B$ respectively, $C$ is middle point of $AB$, then match the followings:-

List I	List II
A) Circle on OA as diameter	$x^2+y^2-ax-by=0$
B) Circle on OB as diameter	$x^2+y^2-ax=0$
C) Circle on AB as diameter	$2x^2+2y^2-ax-by=0$
D) Circle on OC as diameter	$x^2+y^2-by=0$

• A. $2,4,1,3$
• B. $1,2,3,4$
• C. $1,2,4,3$
• D. $4,1,3,2$

Answer 1

The correct option is A $2,4,1,3$

$\frac{x}{a}+\frac{y}{b}=1$
$A(a,0)$ & $B(0,b)$
A) circle on $OA$ as diameter :
From point (13),
So, equation of circle is
$(x-0)(x-a)+(y-0)(y-0)=0$
$\Rightarrow x^2-ax+y^2=0$
B) circle on $OB$ as diameter :
$(x-0)(x-0)+(y-0)(y-b)=0$
$x^2+y^2-yb=0$
C) circle on $AB$ as diameter :
$(x-a)(x-0)+(y-b)(y-0)=0$
$x^2-ax+y^2-by=0$
D) circle on $OC$ as diameter :
$(x-0)(x-\frac{a}{2})+(y-0)(y-\frac{b}{2})=0$
$x+y-\frac{xa}{2}-\frac{yb}{2}=0$
$A\to 2$
$B\to 4$
$C\to 1$
$D\to 3$