Conic Sections Question 121
Question: The angle between the tangents drawn from the points (1,4) to the parabola $ y^{2}=4x $ is
[IIT Screening 2004]
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
Any tangent to $ y^{2}=4x $ is $ y=mx+\frac{1}{m} $
Since it passes throguh (1, 4), we have $ 4=m+\frac{1}{m} $
$ \Rightarrow $ $ m^{2}-4m+1=0 $
$ \Rightarrow $ $ m_1+m_2=4 $ , $ m_1m_2=1 $
$ \Rightarrow $ $ |m_1-m_2|=2\sqrt{3} $
If $ \theta $ is the required angle, then $ \tan \theta =\frac{2\sqrt{3}}{1+1}=\sqrt{3} $
$ \Rightarrow $ $ \theta =\frac{\pi }{3} $ .
BETA
