Question
Question: On the parabola y = x<sup>2</sup>, the point least distance from the straight line y = 2x – 4 is...
On the parabola y = x2, the point least distance from the straight line y = 2x – 4 is
A
(1, 1)
B
(1, 0)
C
(1, -1)
D
(0, 0)
Answer
(1, 1)
Explanation
Solution
Given, parabola y = x2 ... (i)
Straight line y = 2x – 4 ...(ii)
From (i) and (ii), x2 – 2x + 4 = 0
Let f(x) = x2 – 2x + 4, ∴ f’(x) = 2x – 2
For least distance, f’(x) = 0 ⇒ 2x – 2 = 0
⇒ x = 1 From y = x2, y = 1.