Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y2 = – 8x
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 involves y2, so the axis of symmetry is along the x-axis.
The coefficient of x is negative, so the parabola opens to the left. Comparing with the given equation y2 = 4ax, we find that a = 2. Thus the focus of the parabola is (- 2, 0) and the equation of the directrix of the parabola is x = 2. Length of the Latus rectum LL' is 4a = 4 × 2 = 8.

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