Circle And System Of Circles Question 352
Question: The angle between the two tangents from the origin to the circle $ {{(x-7)}^{2}}+{{(y+1)}^{2}}=25 $ is
[MNR 1990; RPET 1997; DCE 2000]
Options:
A) 0
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{6} $
D) $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Any line through (0, 0) be $ y-mx=0 $ and it is a tangent to circle $ {{(x-7)}^{2}}+{{(y+1)}^{2}}=25 $ , if $ \frac{-1-7m}{\sqrt{1+m^{2}}}=5\Rightarrow m=\frac{3}{4},\ -\frac{4}{3} $ . Therefore, the product of both the slopes is -1. i.e., $ \frac{3}{4}\times -\frac{4}{3}=-1 $ .
Hence the angle between the two tangents is $ \frac{\pi }{2} $ .
BETA
