Q. 4 E

# Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolasy2 + 4x + 4y - 3 = 0

Given equation of the parabola is y2 + 4x + 4y - 3 = 0

y2 + 4y = - 4x + 3

y2 + 4y + 4 = - 4x + 7

Comparing with the standard form of parabola (y - a)2 = - 4b(x - c) we get,

4b = 4

b = 1

The vertex is (c, a) =

The focus is (- b + c, a) =

The equation of the axis is y - a = 0 i.e, y + 2 = 0

The equation of the directrix is x - c = b

Directrix is

Directrix is

Directrix is

Length of latus rectum is 4b = 4.

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