If foci of the ellipse x2/a2 + y2/b2 = 1 and hyperbola x2/144 - y2/81=1/25,then the value of b2 is...<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
a) 1
b) 5
c) 7
d) 9
sorry for the mistake, the complete statement is
If foci of the ellipse x2/a2 + y2/b2 = 1 and hyperbola x2/144 - y2/81=1/25 coincide,then the value of b2 is...
a) 1
b) 5
c) 7
d) 9
Lokesh,this problem is not difficult but I think value of a should also have been given in the question because without that ,value of a cannot be determined.Focus of hyperbola is (+or - 3,0)and this is equal to focus of ellipse.If the ellipse given is standard i.e. a>b then it's focus is (+or-ae,0).Now find e of ellipse and if a is given then b can be known.I think you have taken this question from M.L.Khanna.In that book, same type of question is there .
that is the main problem!the value of a is not given,are you sure this problem cannot be solved without value of a?,it may be a tricky question in which answer can be obtained by checking the options!!!!!!!
Eccentricity of ellipse has to be smaller than 1.So, a>+-(3) or a2 has to be greater than 9 .What else can we say?