Tangents are drawn to the hyperbola $4 x^{2}-y^{2}=36$ at the points P and Q . If these tangents intersect at the point $\mathrm{T}(0,3)$ then the area (in sq. units) of $\triangle \mathrm{PTQ}$ is :

JEE Main · 2018 · 08 Apr 2018 · Offline · Hyperbola

Tangents are drawn to the hyperbola

4 x^{2} - y^{2} = 36

at the points P and Q . If these tangents intersect at the point

T (0, 3)

then the area (in sq. units) of

△ PTQ

is :

Answer: (B)

Writing the hyperbola as

\frac{x ^{2}}{9} - \frac{y ^{2}}{36} = 1

, the chord of contact of tangents from

T (0, 3)

\frac{0 \cdot x}{9} - \frac{3 y}{36} = 1

, that is

y = - 12

. Substituting into the hyperbola,

4 x^{2} - 144 = 36

, so

x^{2} = 45

and

x = \pm 35

, placing

P

and

Q

(\pm 35, - 12)

with

P Q = 65

. The height from

T (0, 3)

to the line

y = - 12

15

, so the triangle's area is

\frac{1}{2} \times 65 \times 15 = 455

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option