Conic Sections Question 119
Question: If a circle cuts a rectangular hyperbola $ xy=c^{2} $ in A, B, C, D and the parameters of these four points be $ t_1,\ t_2,\ t_3 $ and $ t_4 $ respectively. Then
[Kurukshetra CEE 1998]
Options:
A) $ t_1t_2=t_3t_4 $
B) $ t_1t_2t_3t_4=1 $
C) $ t_1=t_2 $
D) $ t_3=t_4 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let equation of circle is $ x^{2}+y^{2}=a^{2} $
Parametric form of $ xy=c^{2} $ are $ x=ct,y=\frac{c}{t} $
therefore $ c^{2}t^{2}+\frac{c^{2}}{t^{2}}=a^{2} $
therefore $ c^{2}t^{4}-a^{2}t^{2}+c^{2}=0 $
Product of roots will be, $ t_1t_2t_3t_4=\frac{c^{2}}{c^{2}}=1 $ .
BETA
