`ABCD` is a square in first quadrant whose side is a, taking `AB and AD` as axes, prove that the equation to the circle circumscribing the square is `x^2+ y^2= a(x + y)`.

Options

A. `x^2+y^2=a(x+y)`
B. `2x+y^2=3xy`
C. `x^2+3y^2=xy^2`
D. none of the above

Answer

`x^2+y^2=a(x+y)`

Explanation

As the square is aligned along the axes so the centre of the circle will be the mid point of `AC`



`Rightarrow` `center O = a/2, a/2`

`AC=sqrt((a-0^2)+(a-0^2))=sqrt2a`


Radius of circle `=r=(AC)/2=(sqrt2 a)/2=a/sqrt2`

So, the equation of circle with centre `O` and radius `r` is

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