Maths-
General
Easy
Question
Length of the latus rectum of the parabola whose focus at (2, 3) and directrix is the line x – 4y + 3 = 0 is
- none of these
Hint:
The latus rectum of the parabola is a line segment passing through its focus and perpendicular to its axis. The length of the latus rectum of a parabola is always equivalent to four times the distance of the focus from the vertex of the parabola.
The correct answer is:
Length of the latus rectum of the parabola = ?
directrix is the line x – 4y + 3 = 0
focus = (2, 3)
We know that,
The latus rectum of the parabola is a line segment passing through its focus and perpendicular to its axis.
We know that ,The length of the latus rectum of a parabola is always equivalent to four times the distance of the focus from the vertex of the parabola.
latus rectum of a parabola = 4a { Where a is distance between focus to vertex of parabola. }
And we also know that perpendicular distance from focus (2, 3) on directrix is the line x – 4y + 3 = 0 is equal in length 2a.
so, perpendicular distance from focus (2, 3) on directrix is the line x – 4y + 3 = 0 
but the length of latus rectum of a parabola = 2 x perpendicular distance from focus on directrix = 
-
The length of the latus rectum of the parabola is always equivalent to four times the focal length of the parabola.
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