The angle between the pair of tangents drawn from ( 1 , 1 ) to the circle x 2 + y 2 + 4 x + 4 y - 1 = 0 is

Step-by-step solution

Given equation of circle is x 2 + y 2 + 4 x + 4 y - 1 = 0 Centre - 2 , - 2 O A = O B = r = 4 + 4 + 1 = 3 Where r is radius of circle. O C = 9 + 9 = 3 2 (by distance formula) ⇒ O C 2 = O A 2 + C A 2 (Pythagoras theorem) ⇒ C A 2 = 9 Now, sin α = 3 3 2 = 1 2 ⇒ cos α = 1 2 ⇒ sin 2 α = 2 sin α cos α = 1 ⇒ sin 2 α = sin π 2 ⇒ 2 α = π 2 So π 2 is the required angle between the pair of tangents.