Question

$ABCD$ is a square with side $a$. If $AB$ and $AD$ are along the coordinate axes, then the equation of the circle passing through the vertices $A,B$ and $D$ is

• A. $x^2+y^2=\sqrt{2}a(x+y)$
• B. $x^2+y^2=\frac{a}{\sqrt{2}}(x+y)$
• C. $x^2+y^2=a(x+y)$
• D. $x^2+y^2=a^2(x+y)$
• E. $a(x^2+y^2)=x+y$

Answer 1

The correct option is C $x^2+y^2=a(x+y)$

Equation of the circle passing through $(0,0),(a,0),(0,a)$ will be

$x^2+y^2+2gx+2fy+c=0$ ....(i)

Equation (i) passes through all the above points.

Then, $c=0,2g=-a$ and $2f=-a$

Therefore, equation of the circle will be

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

$\Rightarrow x^2+y^2=a(x+y)$