UPSC NDA Math Model Paper 8

Given: The hyperbola is centred at origin i.e O (0, 0), length of transverse axis is 6 and one focus is (0, 4).
∵ The foci of the given hyperbola are of the form (0, ± c), it is a vertical hyperbola i.e it is of the form:

y2

a2

−

x2

b2

=1
⇒c=4 and c2=16
As we know that, the length of tranverse axis of the hyperbola of the form

y2

a2

−

x2

b2

=1 is given by: 2a
⇒2a=6
⇒a=3 and a2=9
As we know that b2=c2−a2
⇒b2=16−9=7
Hence, the equation of required hyperbola is:

y2

9

−

x2

7

=1