Question

The equation of the circumcircle of the triangle by the lines $x=0,y=0,\frac{x}{a}+\frac{y}{b}=1$ is

• A. $x^2+y^2+ax-by=0$
• B. $x^2+y^2-ax+by=0$
• C. $x^2+y^2-ax-by=0$
• D. $x^2+y^2+ax+by=0$

Answer 1

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

The required circumcircle is drawn through $A$ and $B$ and $\angle AOB={90}^0$, $\because o$ is origin, $\Rightarrow AB$ subtends ${90}^0$ at the circumference.

Hence $AB$ must be the diameter of the circle.

$\therefore$ Centre of circle $\to (\frac{a+0}{2},\frac{0+b}{2})$

$\Rightarrow (\frac{a}{2},\frac{b}{2})$

$\therefore$ Equation of circle:

$x^2+y^2+2\left(\frac{-a}{2}\right)x+2\left(\frac{-b}{2}\right)y+c=0$

$\Rightarrow x^2+y^2-ax-by+c=0$

$\because$ Circle passes through origin,

$\Rightarrow c=0$

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