ABCD is a square of side 'a'. If AB and AD are taken as co-ordinate axes, prove that the equation of the circle circumscribing the square is `x^2+y^2=a(x+y)`.

Explanation

`therefore` Centre of the circle is at (a/2, a/2) and radius is `(asqrt2)/2=a/sqrt2`
`therefore` Equation of the circle is
`(x-a/2)^2+(y-a/2)^2=a^2/2`
or, `x^2+a^2/4-ax+y^2+a^2/4-ay=a^2/2`
or, `x^2+y^2-ax-ay=0`
or, `x^2+y^2=a(x+y)`