Multiple choice

Find the intervals of values of $'a'$ for which the line $(y+x)=0$ bisects two chords drawn from a point $\left( \cfrac { 1+\sqrt { 2 } a }{ 2 } ,\cfrac { 1-\sqrt { 2 } a }{ 2 } \right) $ to the circle $(2{x}^{2}+2{y}^{2}-(1+\sqrt { 2 } a)x-(1+\sqrt { 2 } a)y)=0$

  1. $a\in (-\infty,-2)\cup (2,\infty)$
  2. $a\in (-2,2)$
  3. $a\in (-\infty,-4)\cup (4,\infty)$
  4. $a\in [-2,2]$
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