The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the y-axis is

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xy1+y+1=0

xy1−2y-2=0

xy1−y-1=0

yy1+2xy+1=0

answer is B.

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Detailed Solution

x2=4a(y+1)−c ..............(i)⇒2x=4adydx⇒4a=2xy1.............(ii) From 1 and 2⇒xy1−2y−2=0

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