The length of latus rectum of the parabola whose focus is (u2/2g sin2α , -u​2/2g cos2α) and the directrix is y= u2/2g is

u2/g cosα
u2/g cos22α
2u2/g cos2α
2u2/g cos2α

Dear Student,
Please find below the solution to the asked query:

We have focus asSu22gsin2α, -u22gcos2αEquation of directrix:y=u22gy-u22g=00x+y-u22g=0Perpendicular distance between focus and directrix is given by:p=0.u22gsin2α+1.-u22gcos2α-u22g02+1=-u22gcos2α-u22g1=-u22gcos2α+u22g=u22gcos2α+u22g=u22gcos2α+1=u22g2cos2α-1+1=u22g2cos2α=u22g2cos2αp=u2cos2αgNow length of latus ractum is twice the perpendicular distance between focus and directrix.Length of latus ractum=2p=2u2cos2αgHence last option is correct.

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