Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Solve this problem Tangents are drawn to the hyperbola4x2−y2=36 at the points P and Q. If thesetangents intersect at the point T(0, 3) thenthe area (in sq. units) of ΔPTQ is :

Tangents are drawn to the hyperbola
4x2−y2=36 at the points P and Q. If these
tangents intersect at the point T(0, 3) then
the area (in sq. units) of ΔPTQ is :

  • Option 1)

    36\sqrt{5}

  • Option 2)

    45{\sqrt{5}}

  • Option 3)

    54{\sqrt3}

  • Option 4)

    60{\sqrt3}

 

Answers (1)

best_answer

 

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

T = 0\Rightarrow 0-\frac{3y}{36}=1

y=-12

if y=-12  in \frac{x^{2}}{9}-\frac{y^{2}}{36}= 1

x = \pm 3\sqrt5

Thus \Delta PTQ = 1/2 \times 6\sqrt5\times 15

=45\sqrt5

 

Equation of Tangent to Hyperbola -

\frac{xx_{1}}{a^{2}}-\frac{yy_{1}}{b^{2}}= 1

- wherein

For the Hyperbola

\frac{x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}= 1 and

P\left ( x_{1} ,y_{1}\right )

 

 


Option 1)

36\sqrt{5}

This is incorrect

Option 2)

45{\sqrt{5}}

This is correct

Option 3)

54{\sqrt3}

This is incorrect

Option 4)

60{\sqrt3}

This is incorrect

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

JEE Mains: Farmer's son from remote Maharashtra village aces exam

Latest Question