A) \[-9\]
B) 9
C) \[-3\]
D) 3
Correct Answer: B
Solution :
[b] \[\because {{y}^{2}}=12x\] ......(1) \[\because \]The general equation of parabola be \[{{y}^{2}}=4ax\] ......(2) Comparision (1) & (2), we have \[\therefore 4a=12\] \[\therefore a=3.\] If \[~y=mx+k\] be the normal to the parabola \[{{y}^{2}}=12x\] then \[k=-2am-a{{m}^{3}}\] (By condition of normality) \[\therefore \]Given equation of normal be \[x+y=k\Rightarrow y=-x+k\] Here, \[m=-1\And a=3\] \[\therefore k=-2.3\left( -1 \right)-3.{{\left( -1 \right)}^{3}}\] \[=6+3.1=6+3=9\]. Hence, option [b] is correct.
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