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afeasfaerw23231233 · #1 June 14th, 2008, 05:54 AM

bk2 p105 q27
question : the vertices of a quadrilateral are the centres of the circles:
$C_1 : x^2 +y^2+2tx=0$
$C_2: x^2+y^2 +\frac {2y}t = 0$
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
$0,- \frac 1 t$
0,0
$-\frac {2t}{1+t^4} , -\frac {2t^3 }{1+t^4}$
area:
$\frac 1 2 \begin{vmatrix} 0 & 0 \\ -t & 0 \\ 0 & -\frac 1 t \\-\frac {2t}{1+t^4} & -\frac {2t^3 }{1+t^4}\\0 & 0\end{vmatrix}$
$= \frac 1 2 (\frac {t^4-1}{1+t^4})$
cannot prove that the area is a constant
thanks