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Question
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola:
y2 = 8x
Solution
Given:
y2 = 8x
On comparing the given equation with
\[y^2 = 4ax\]
\[4a = 8 \Rightarrow a = 2\]
∴ Vertex = (0, 0)
Focus = (a, 0) = (2, 0)
Equation of the directrix:
x = −a
i.e. x = −2
Axis = y = 0
Length of the latus rectum = 4a = 8
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