Question

Shortcut to find latus rectum when directrix and focus is given

Answer 1

Answer:

We all know that latus rectum is the distance between fochs and vertex or 4 times the distance between focus and directrix.

let me show this shortcut with an example:

let focus be, say,=(-1,1)

and directrix be, say ,::: 4x+3y-24=0

distance between focus and directrix is::::

=|4×(-1) + 3×1 - 24 |/(4^2 +3^2)^1/2

= |-4+3-24|/|5|

=|-25/5|

= 5

so the latus rectum is 4times of this

= 4× 5

=20

hope this trick helps uh