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Question

For the parabola
x2+8x+12y+4=0, which of the following options is/are correct?

A
length of latus rectum is 12 units
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B
coordinates of vertex are (4,1)
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C
length of latus rectum is 16 units
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D
coordinates of vertex are (4,2)
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Solution

The correct option is B coordinates of vertex are (4,1)
The equation of parabola is
x2+8x+12y+4=0(x+4)216+12y+4=0(x+4)212+12y=0(x+4)2=12y+12(x+4)2=12(y1)
Let x+4=X,y1=Y
X2=12Y
Comparing it with x2=4ay, we get
a=3
and vertex as (X,Y)(0,0)
X=0,Y=0
x+4=0,y1=0
x=4,y=1

Vertex of given parabola is (4,1)

Length of latus rectum=4a=4×3=12

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