bk2 p105 q27

question : the vertices of a quadrilateral are the centres of the circles:

$\displaystyle C_1 : x^2 +y^2+2tx=0 $

$\displaystyle C_2: x^2+y^2 +\frac {2y}t = 0$

and their intersecting points

a) find the coordinates of the vertices of the quadrilaterl.

b) find that the area of the quadrilateral is a constant.

my working

vertices :

-t, 0

$\displaystyle 0,- \frac 1 t $

0,0

$\displaystyle -\frac {2t}{1+t^4} , -\frac {2t^3 }{1+t^4}$

area:

$\displaystyle \frac 1 2 \begin{vmatrix}

0 & 0 \\

-t & 0 \\

0 & -\frac 1 t \\

-\frac {2t}{1+t^4} & -\frac {2t^3 }{1+t^4}\\

0 & 0

\end{vmatrix}$

$\displaystyle = \frac 1 2 (\frac {t^4-1}{1+t^4})$

cannot prove that the area is a constant

thanks