Question

If the tangents at the points P and Q on the circle x² + y² – 2x + y = 5 meet at the point R  \(( \frac{9}{4},2 ) \)then the area of the triangle PQR is 

• A. \(\frac{13}{8}\)
• B. \(\frac{13}{4}\)
• C. \(\frac{5}{8}\)
• D. \(\frac{5}{4}\)

Answer 1

The Correct Option is C

The equation of the circle is: \[ x^2 + y^2 - 2x + y = 5 \] 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: \[ 5x + 10y - 25 = 0 \] Using the distance formula, the area of triangle \(PQR\) is given by: \[ \text{Area} = \frac{1}{2} \times (P'Q) \times (PQ) \] After calculating the distances, we find: \[ \text{Area} = \frac{5}{4} \]