JEE Mathematics 2023 Question with Solution

Given: The circle is $x^2 + y^2 - 2x + y = 5$ and the tangents at points P and Q meet at $R\left(\frac{9}{4}, 2\right)$.

Find: The area of triangle PQR.

The equation of the circle is:

The equation of the line joining the points $P$ and $Q$ is derived using the coordinates of the points. We find the equation of the line to be:

Using the distance formula, the area of triangle $PQR$ is given by:

After calculating the distances, we find:

Therefore, the area of triangle PQR is $\frac{5}{4}$, so the correct option is C.

Given: The tangents from $R\left(\frac{9}{4}, 2\right)$ touch the circle at $P$ and $Q$.

Find: The area of triangle $PQR$.

From the extracted solution, the chord of contact $PQ$ is taken as:

Then the area is evaluated using the distance-based relation mentioned in the solution:

The final computed value given in the solution is:

Hence, the correct answer is $\frac{5}{4}$.