find the length of latus rectum ofellipse with foci
(-2,-1) and (1,2) and directrix x+y=5????????

Hi Vishal,

This is the method.

Centre of the ellipse is the midpoint od the focii = (-1/2,1/2)

From centr to Focus distance = ae --------(1)

And from centre to directrix = a/e ---------(2)

So use distance formula and find (1)

And using distance of point from the line find (2)

Multiply both and find a. Divide both and find e.

So now length of latus rectum = 2b²/a = 2a(1-e²).

Substitute and find the lenght of the latus rectum.

Hope this helps. All the best.

Regards,

Ashwin (IIT Madras).