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