Question
Question: The point on the curve y<sup>2</sup> = 4x which is nearest to (2, 1) is...
The point on the curve y2 = 4x which is nearest to (2, 1) is
A
(4, 4)
B
(1, 2)
C
(9,6)
D
(4, 6)
Answer
(1, 2)
Explanation
Solution
Let P = (t2, 2t) and Q = (2, 1)
PQ2 = (t2 – 2)2 + (2t – 1)2
For the minimum value of PQ
(PQ2)1 = 0 ⇒ 4t(t2 – 2) + 4(2t – 1) = 0
⇒ t3 = 1 t = 1
(PQ2)11 = 3t2> 0 when t = 1
∴ PQ is minimum when t = 1
∴ The nearest point is (t2, 2t) = (1, 2)
