Question
An ellipse and a hyperbola have the same centre “origin”, the same foci. The minor-axis of the one is the same as the conjugate axis of the other. If e1, e2 be their eccentricities respectively, then 
+ 
is equal to
- 1
- 2
- 4
- 3
Hint:
find the expression for the eccentricities of the ellipse and the hyperbola using the given conditions.
The correct answer is: 2
2
Centre : (0,0)
Foci : ellipse : (a1e1,0)
Hyperbola : (a2e2,0)
2a1 = 2a2 (minor axis equal to conjugate axis)
a1e1=a2e2
e12= a12-b2/a12
e22= a22+b2/a22
this gives us 1/ e12+ 1/ e22 = 2e2/e2 = 2
the conjugate axis of a hyperbola is the line through the center of the hyperbola and perpendicular to the line joining the focii.
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