Question

$ABCD$ is a square whose side is $a$. The equation of the circle circumscribing the square, taking $AB$ and $AD$ as the axes of reference is

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

Answer 1

Answer: (C)

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

$AB$ on x-axis and $AD$ on y-axis.

centre of circle $=(\frac{a}{2},\frac{a}{2})$.

Diameter of circle $=$ Diagonal of square $=\sqrt{2}a$

Radius $=\frac{a}{\sqrt{2}}$

Equation of circle -

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

$x^2+y^2+\frac{a^2}{4}+\frac{a^2}{4}-ax-ay=\frac{a^2}{2}$

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