1. (2002 Hunan Province Competition Question) Given a moving point $P(x, y)$ satisfies the quadratic equation $10 x-2 x y-2 y+1=0$. Then the eccentricity of this quadratic curve is $\qquad$.
1. Fill in $\sqrt{2}$. Reason:

From $10 x-2 x y-2 y+1=0$ we have
$$
x^{2}+6 x+y^{2}-6 y-2 x y+9=x^{2}-4 x+4+y^{2}-4 y+4 \text {. }
$$

This implies $\sqrt{(x-2)^{2}+(y-2)^{2}}=|x-y+3|$,
which means $\frac{\sqrt{(x-2)^{2}+(y-2)^{2}}}{\frac{|x-y+3|}{\sqrt{2}}}=\sqrt{2}$, hence $e=\sqrt{2}$.