SATHEE: Hyperbola 2 Question 5

Hyperbola 2 Question 5

5.

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 $△ P T Q$ is

(a) $45 \sqrt{5}$

(b) $54 \sqrt{3}$

(d) $36 \sqrt{5}$

(2018 Main)

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Answer:

Correct Answer: 5. (a)

Solution:

Tangents are drawn to the hyperbola $4 x^{2} - y^{2} = 36$ at the point $P$ and $Q$ .

Tangent intersects at point $T (0, 3)$

Clearly, $P Q$ is chord of contact.

$∴$ Equation of $P Q$ is $- 3 y = 36$

$\Rightarrow y = - 12$

Solving the curve $4 x^{2} - y^{2} = 36$ and $y = - 12$ ,

we get $x = \pm 3 \sqrt{5}$

Area of $△ P Q T = \frac{1}{2} \times P Q \times S T = \frac{1}{2} (6 \sqrt{5} \times 15) = 45 \sqrt{5}$

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Hyperbola 2 Question 5

5.

Answer:

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