AP EAPCET 08-Jul-2022 Shift 2 Paper

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)=

1

2

×base×height
=

1

2

×PQ×OM=

1

2

×4b×2a
=4ab