A) \[x=-1\]
B) \[x=1\]
C) \[x=-\frac{3}{2}\]
D) \[x=\frac{3}{2}\]
Correct Answer: D
Solution :
The equation of parabola is \[{{(y+2)}^{2}}=-4\left( x-\frac{1}{2} \right)\] Shifting the origin\[\left( \frac{1}{2},\,\,-2 \right)\], the equation of parabola becomes\[{{Y}^{2}}=-4X\] where \[X=x-\frac{1}{2},\,\,Y=y+2\] An equation of its directrix is\[X=1\]. \[\therefore \]Required directrix,\[x=\frac{3}{2}.\]
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