A) \[(-1,-\sqrt{2})\]
B) \[(2\sqrt{2},-1)\]
C) \[(-4,4\sqrt{2})\]
D) \[(4,4\sqrt{2})\]
Correct Answer: C
Solution :
Given parabola \[{{y}^{2}}=-8x,\]compare with \[{{y}^{2}}=4ax,\] we get \[4a=-8\] \[\Rightarrow \] \[a=-2\] We know that if one of a focal chord is \[(a{{t}^{2}},2at),\] then the other end will be \[(a/{{t}^{2}},\,-2a/t).\] Here, one end is \[(-1,2\sqrt{2})\] \[\therefore \] \[a{{t}^{2}}=-1\] \[\Rightarrow \] \[{{t}^{2}}=\frac{1}{2}\] \[\Rightarrow \] \[t=\frac{1}{\sqrt{2}}\] So, other end \[=\left( \frac{-2}{1/2},\frac{-2\times -2}{1/\sqrt{2}} \right)\] \[=(-4,\,4\sqrt{2})\]
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