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प्रश्न
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
4x2 + y = 0
उत्तर
Given:
4x2 + y = 0
\[\Rightarrow \frac{- y}{4} = x^2\]
On comparing the given equation with \[x^2 = - 4ay\]
\[4a = \frac{1}{4} \Rightarrow a = \frac{1}{16}\]
∴ Vertex = (0, 0)
Focus = (0, −a) = \[\left( 0, \frac{- 1}{16} \right)\]
Equation of the directrix:
y = a
i.e. \[y = \frac{1}{16}\]
Axis = x = 0
Length of the latus rectum = 4a =\[\frac{1}{4}\]
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