The lactus rectum of a parabola is a line segment passing through the focus of the parabola......?
The lactus rectum of a parabola is a line segment passing through the focus of the parabola such that the segment is parallel to the directrix and has both endpoints on the parabola. Show that the lactus rectum of the graph of the equation y=a(x-h)^2 +k has the length 1/a.
The lactus rectum of a parabola is a line segment passing through the focus of the parabola such that the segment is parallel to the directrix and has both endpoints on the parabola. Show that the lactus rectum of the graph of the equation y=a(x-h)^2 +k has the length 1/a.
1 Answer
Pleasesee below.
Explanation:
The equation of parabola is
hence vertex is
This is the equation of a vertical parabola. In such parabolas, for the equation is of the type
So let us convert the given equation
Hence, focus is
As axis of symmetry is
Let us find the two points, where this line
i.e.
the two points at which line parallel to directrix cuts parabola are
As ordinate is same, length of latus rectum is
=
=