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0 votes
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in Mathematics by (53.3k points)

Find the vertex, focus, directrix and latus rectum of the parabola y2 + 4x - 2y + 3 = 0.

1 Answer

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by (53.1k points)
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Best answer

The given equation is written as

(y - 1)2 = -4(x + 1/2)

Let X = x + 1/2 and Y = y -1

Then we have

Y2 = -4X 

 Therefore, the vertex is given by

(X = 0,Y = 0) = (-1/2, 1)

 Since a = 1, the focus (X = −1, Y = 0) is

X = a or x + 1/2 = 1 or x - 1/2 = 0

 The latus rectum is given by 4a = 4

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