Conic Sections Question 188
Question: The length intercepted by the curve $ y^{2}=4x $ on the line satisfying $ dy/dx=1 $ and passing through point (0, 1) is given by
[Orissa JEE 2005]
Options:
A) 1
B) 2
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let equation of line is $ y=ax+b $ ; $ \frac{dy}{dx}=a=1 $ given Also $ y=ax+b $ passing through (0, 1) $ b=1 $
So required line be $ y=x+1 $
Now point of intersection of the line and parabola gives $ x^{2}+2x+1=4x $
therefore $ x^{2}-2x+1 $
therefore $ x=1 $ $ y=2 $
Line touch that parabola. Length intercepted is equal to 0.
BETA
