Conic-Sections Question 571
Question: The normal at the point $ (bt^2_1,2bt_1) $ on a parabola meets the parabola again in the point $ (bt^2_2,2bt_2) $ Then
Options:
A) $ t_2=t_1+\frac{2}{t_1} $
B) $ t_2=-t_1-\frac{2}{t_1} $
C) $ t_2=-t_1+\frac{2}{t_1} $
D) $ t_2=t_1-\frac{2}{t_1} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Equation of the normal to a parabola $ y^{2}=4bx $ at point $ ( bt^2_1,2bt_1 ) $ is $ y=-t_1x+2bt_1+bt^3_1 $ As given, it also passes through $ ( bt^2_2,2bt_2 ) $ then $ 2bt_2=-t_1bt^2_2+2bt_1+bt^3_1 $
$ \Rightarrow 2=-t_1(t_2+t_1)\Rightarrow t_2+t_1=-\frac{2}{t_1} $
$ \Rightarrow t_2=-t_1-\frac{2}{t_1} $
BETA
