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mathematics

mathematics

by Nehil Jain -
Number of replies: 1
a rectangular hyperbola passes through the point (0,0) and has one of its focus at (1,0), thge latus rectum is 2 units. the locus of the other focus is:-
In reply to Nehil Jain

Re: mathematics

by Chandni Bhatia -
Hi,Nehil.I think the question is asking about the coordinates of the other focus.For a rectangular hyperbola,e=root2.Let the hyperbola be (x-h)2 - (y-k)2=a2.Then it's focus in general is given by: [h(+/-) ae,k].One of the focus is [1,0].So,k=0.Also,the hyperbola passes through (0,0).From this we get h=(+/-)a.So the focus is [(+/-){a+ae},0].Hence the given focus is the one which is positive i.e. a+ae=1,e=root2.From this we get a=root2 -1.Other focus is [-(a+ae),0]So the other focus is (-1,0).Please reply if the answer is correct or not.Also please tell if the question is asking about the coordinates of the other focus or is asking about something else.