Let tangents are drawn from A(a,0) to the hyperbola
x2
a2
−
y2
b2
=2 PQ is the chord of contact. Asymptotes are A1 and A2 Equation of Ai and A2 are
x
a
−
y
b
=0 and
x
a
+
y
b
=0 respectively. Equation of PQ is given by
xx1
a2
−
yy1
b2
=2 ⇒
ax
a2
−0=2⇒x=2a Now solving x=2a and asymptotes A1 and A2, we get P≡(2a,2b) and Q≡(2a,−2b) ⇒M is the mid-point of PQ ⇒M≡(2a,0) ⇒OM=2a and PQ=4b ∴Area (△OPQ)=