Conic Sections Question 279
Question: On the parabola $ y=x^{2} $ , the point least distance from the straight line $ y=2x-4 $ is
[AMU 2001]
Options:
A) (1, 1)
B) (1, 0)
C) (1, -1)
D) (0, 0)
Show Answer
Answer:
Correct Answer: A
Solution:
Given, parabola $ y=x^{2} $ ……(i) Straight line $ y=2x-4 $ ……(ii) From (i) and (ii), $ x^{2}-2x+4=0 $
Let $ f(x)=x^{2}-2x+4 $ , $ f’(x)=2x-2 $ . For least distance, $ f’(x)=0 $
$ \Rightarrow 2x-2=0 $
therefore $ x=1 $
From $ y=x^{2} $ , $ y=1 $
So the point least distant from the line is (1, 1).
BETA
