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Question

Find the vertex, axis focus, directrix and latus rectum of the parabola y2+4x+4y3=0.

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Solution

Y2+4y+4x3=0

(y+2)24+4x3=0

(y+2)2=4(x74)

Let Y=y+2,X=x74

Then we have

Y2=4x

Comparing the gives equation with Y2=4ax

4a=4a=1

vertex =(X=0,Y=0)=(x=74,y=2)

Focus =(X=a=1,Y=0)(x74=1,y+2=0)=(x=34,y=2)

Equation of directrix

X=a=1

i.e x74=1x=114

Axis =Y=0

i.e y+2=0y=2

length of the latus rectum =4a=4 units

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