A) \[8\sqrt{2}\]
B) \[6\sqrt{3}\]
C) \[3\sqrt{2}\]
D) \[2\sqrt{11}\]
Correct Answer: B
Solution :
Parabola \[{{x}^{2}}=4y\] .... (i) Chord \[x-\sqrt{2}y+4\sqrt{2}=0\] .... (ii) Solving (i) & (2) \[{{(\sqrt{2})}^{2}}\,{{(y-4)}^{2}}=4y\] \[\Rightarrow \,\,\,\,2{{y}^{2}}-16y+32=4y\] \[\Rightarrow \,\,\,\,2{{y}^{2}}-20y+32=0\] \[\Rightarrow \,\,\,\,\,\,\,{{y}^{2}}-10y+16=0\] \[\Rightarrow \,\,\,\,\left( y-2 \right)\left( y-8 \right)=0\] \[y=2~~~~~and~~~~y=8\] \[\begin{align} & from\,(2)\,\,x=-2\sqrt{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=4\sqrt{2} \\ & A(-2\sqrt{2},\,\,2)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B(4\sqrt{2},\,\,\,8) \\ & \, \\ \end{align}\] Length of chord = distance between A and B \[=\,\,\sqrt{{{\left( 6\sqrt{2} \right)}^{2}}+{{\left( 6 \right)}^{2}}}\] \[=\,\,\,\,6\sqrt{3}\]
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