Conic Sections Question 158
Question: If $ x+y=k $ is a normal to the parabola $ y^{2}=12x $ , then k is
[IIT Screening 2000]
Options:
A) 3
B) 9
C) -9
D) -3
Show Answer
Answer:
Correct Answer: B
Solution:
Any normal is $ y+tx=6t+3t^{3}. $ It is identical with $ x+y=k $ if $ \frac{t}{1}=\frac{1}{1}=\frac{6t+3t^{3}}{k} $
$ \therefore $ $ t=1 $ and $ (a,\pm 2a). $
therefore $ k=9. $
BETA
