Binomial Theorem


In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.
straight y squared equals negative 8 straight x


space space straight y squared equals negative 8 straight x
It is the equation of a parabola in the standard form straight y squared equals negative 4 ax comma space straight a greater than 0 and open towards the left.
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The focus is straight S space left parenthesis negative straight a comma space 0 right parenthesis space left right arrow space left parenthesis negative 2 comma space 0 right parenthesis
The equation of axis of parabola is y = 0 (x-axis).
The equation of directrix is x - a = 0 or x - 2 = 0
The length of latus rectum = 4a = 4 space cross times space 2 equals 8

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