CONCEPT: The eccentricity of a hyperbola of the form
y2
a2
−
x2
b2
=1 is given by: e=√1+
b2
a2
CALCULATION: Given: The point (3tanθ,2secθ ) lies on the hyperbola. As we can see that, if we substitutex=3tanθ and y=2secθ in the expression
y2
4
−
x2
9
we get ⇒
y2
4
−
x2
9
=sec2θ−tan2θ=1 So, we can say that, the point (3tanθ,2secθ ) lies on the hyperbola
y2
4
−
x2
9
=1 As we know that, eccentricity of the hyperbola of the form