Ex: The angle between the two tangents from the origin to the circle (x − 7)2 + (y + 1)2 = 25 is
A) 0
B) π/3
C) π/6
D) π/2
Correct answer: D
Explanation & Trick:
Any line through (0, 0) be y − mx = 0 and it is a tangent to circle (x−7)2 + (y+1)2 = 25, if
− 1 − 7m / √1+m2 =5 ⇒ m = 3 / 4, −4 / 3
Therefore, the product of both the slopes is -1.
i.e., 3 / 4 × − 4 / 3 = −1.
Hence the angle between the two tangents is π / 2.
