UPSC NDA Math Model Paper 2

Since the coordinates of the one focus at (0, 4) = (0 , ±c ), it is a case of vertical hyperbola
⇒ c = 2
It is a case of vertical hyperbola
⇒ The equation of hyperbola is

y2

b2

−

x2

a2

=1 .......(1)
Length of the transverse axis = 6
⇒2a=6
⇒a=3
Also c2=a2+b2
⇒22=32+b2
⇒b2=7
Equation (1) becomes

y2

9

−

x7

7

=1
Hence, The equation of the hyperbola with center at the origin, length of the transverse axis is 6 and one focus at (0, 4) is

y2

9

−

x7

7

=1