In each of the following, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

y2 = – 8x


The given equation is y2 = -8x


Here, the coefficient of x is negative.


Hence, the parabola open towards the left.


On comparing this equation with y2 = -4ax, we get,


-4a = -8


a = 2


Thus,


Co-ordinates of the focus = (-a,0) = (-2, 0)


Since, the given equation involves y2, the axis of the parabola is the x-axis.


Equation of directrix, x =a, then,


y = 2


Length of latus rectum = 4a = 8


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