The shortest distance between the line and the curve is
- A.2
- B.
- C.
- D.
Show answer and solution
Correct option: C
Solution
On the parabola y² = x - 2, parameterize as x = t² + 2, y = t. The distance from point (t² + 2, t) to the line x - y = 0 is |t² + 2 - t|/√2.
Minimize f(t) = t² - t + 2: f'(t) = 2t - 1 = 0 → t = 1/2.
Minimum value = (1/4) - (1/2) + 2 = 7/4.
Shortest distance = (7/4)/√2 = 7/(4√2).
Minimize f(t) = t² - t + 2: f'(t) = 2t - 1 = 0 → t = 1/2.
Minimum value = (1/4) - (1/2) + 2 = 7/4.
Shortest distance = (7/4)/√2 = 7/(4√2).
[JEE Main 2019 · 8 April · Shift I]