Conic Sections Question 82
Question: The angle between the tangents drawn from the origin to the parabola $ y^{2}=4a(x-a) $ is
[MNR 1994]
Options:
A) $ 90^{o} $
B) $ 30^{o} $
C) $ {{\tan }^{-1}}\frac{1}{2} $
D) $ 45^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
Any line through origin is $ y=mx $ Since it is a tangent to $ y^{2}=4a(x-a), $ it will cut it in one coincident point. Roots of $ m^{2}x^{2}-4ax+4a^{2}=0 $ are equal. $ 16a^{2}-16a^{2}m^{2}=0 $ or $ m^{2}=1 $ or $ m=1,-1 $
Product of slopes $ =-1 $ .
Hence it is a right angled triangle.
BETA
