When the axis of symmetry is along the x-axis the parabola opens to the
o right if the coefficient of x is positive, o left if the coefficient of x is negative.
When the axis of symmetry is along the y-axis the parabola opens
o upwards if the coefficient of y is positive. o downwards if the coefficient of y is negative.
Latus Rectum of Parabola
Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola.
Length of latus rectum of the parabola y 2 = 4ax, is 4a
Numerical: Find the coordinates of the focus, axis, the equation of the directrix and latus rectum of the parabola y 2 = 8x.
Solution: the parabola equation involves y 2, so the axis of symmetry is along the x-axis.
The coefficient of x is positive so the parabola opens to the right. Comparing with the given equation