Let the centre of a circle C be α , β and its radius r < 8 . Let 3 x + 4 y = 24 and 3 x – 4 y = 32 be two tangents and 4 x + 3 y = 1 be a normal to C . Then ( α - β + r ) is equal to

Step-by-step solution

Given, The centre of a circle C be α ,   β and its radius r   <   8 , And 3 x + 4 y = 24 and 3 x – 4 y = 32 be two tangents So, the distance from centre will be radius, 3 α + 4 β - 24 5 = 3 α - 4 β - 32 5 Taking + sign we get, ⇒ 3 α + 4 β - 24 = 3 α - 4 β - 32 ⇒   8 β = - 8 ⇒ β = - 1 And taking - sign we get, 3 α + 4 β - 24 = - 3 α + 4 β + 32 ⇒ 6 α = 56 ⇒ α = 56 6 And