If the tangents at the points P and Q on the circle x 2 + y 2 - 2 x + y = 5 meet at the point R 9 4 , 2 , then the area of the triangle P Q R is

Step-by-step solution

Given, The tangents at the points P and Q on the circle x 2 + y 2 - 2 x + y = 5 meet at the point R 9 4 ,   2 , Now plotting the diagram of the above data we have, Now we know that, Length of tangent is given by, P R = Q R = S 1 So, L = S 1 = 9 4 2 + 2 2 - 2 × 9 4 + 2 - 5 ⇒ L = 5 4 Now distance between C R will be, C R = 9 4 - 1 2 + 2 + 1 2 2 = 25 16 + 25 4 = 125 16 = 5 5 4 Now finding P Q by equating area, we get 1 2 × 5 2 × L = 1 2 × P Q 2 × C R ⇒ 1 2 × 5 2 × 5