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 .