y 2 = 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 is 4a = 4 × 2 = 8.
Numerical: Find the equation of the parabola with vertex at( 0, 0) and focus at( 0, 2).
Solution: Since the vertex is at( 0,0) and the focus is at( 0,2) which lies on y-axis, the y-axis is the axis of the parabola. Therefore, equation of the parabola is of the form x 2 = 4ay.
Thus, we have x 2 = 4( 2) y, i. e., x 2 = 8y Terms used in Ellipse
o The two fixed points are called the foci( plural of‘ focus’) of the ellipse o The midpoint of line segment joining foci is called the centre of the ellipse. o The line segment through the foci of the ellipse is called the major axis. o The line segment through centre & perpendicular to major axis is called minor axis. o The end points of the major axis are called the vertices of the ellipse.