NDA Math Conic Section

Consider the given equation of the hyperbola and the point lying on it.The length of the latus rectum will be

2b2

a

=

4

3

∴b2=

2

3

a
Now, considering the equation of the hyperbola and the point lying on it,we get

x2

a2

−

y2

b2

=1
P(3√5,1)
Substituting the given point in the equation of the hyperbola, we get

45

a2

−

1

b2

=1

45

a2

−

3

2a

=1
90−3a=2a2
2a2+3a−90=0
a=6(taking positive value)
∴b=√

2a

3

=√

2×6

3

=2

x2

a2

−

y2

b2

=1
⇒

x2

62

−

y2

22

=1
Conjugate axis length =2b=2(2)=4