If the tangents at the points P and Q are the circle meet at the point R , then the area of the triangle PQR is:

5/8 Explanation: Eqn. of chord of contact PQ=

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

If the tangents at the points P and Q are the circle $x^{2} + y^{2} - 2 x + y = 5$ meet at the point R $(\frac{9}{4}, 2)$ , then the area of the triangle PQR is:

Choose the correct answer:

A.
5/4
B.
13/4
C.
5/8
(Correct Answer)
D.
13/8

Correct Answer:

5/8

Explanation

$\frac{9}{4} x + 2 y - (x + \frac{9}{4}) + \frac{1}{2} (y + 2) - 5 = 0$

$\Rightarrow x + 2 y = 5$

$A r e a = \frac{1}{2} \times \frac{5}{4} \times 5 = \frac{5}{8}$

Eqn. of chord of contact

$x_{1} x + y_{1} y + g (x + x_{1}) + f (y + y_{1}) + c = 0$

PQ= $2 r^{2} - p = 5$

Explanation

$\frac{9}{4} x + 2 y - (x + \frac{9}{4}) + \frac{1}{2} (y + 2) - 5 = 0$

$\Rightarrow x + 2 y = 5$

$A r e a = \frac{1}{2} \times \frac{5}{4} \times 5 = \frac{5}{8}$

Eqn. of chord of contact

$x_{1} x + y_{1} y + g (x + x_{1}) + f (y + y_{1}) + c = 0$

PQ= $2 r^{2} - p = 5$

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