UPSC NDA Math Model Paper 1

Here, we have to find the equation of the hyperbola whose foci are (±√29,0) and the transverse axis is of length 10.
By comparing the foci (±√29,0) with (± ae, 0)
⇒ae=√29
∵ The length of transverse axis is 10
⇒2a=10⇒a=5
⇒5e=√29
⇒e2=29∕25
As we know that, e=

√a2+b2

a

⇒a2e2=a2+b2
⇒b2=29−25=4
So, the equation of the hyperbola is

x2

25

−

y2

4

=1
Hence, option B is the correct answer.