Question

The least distance of the point (3, 2) from the parabola y = x² + 2 is

• A. $\sqrt{3}$
• B. $\sqrt{5}$
• C. $2\sqrt{3}$
• D. $2\sqrt{5}$

Answer 1

Answer: (B)

$\sqrt{5}$

Answer 2

Let P(x, x²+2) be the nearest point of Q(3, 2) on the given parabola. Then

PQ² = (x – 3)² + x⁴

(PQ²)¹ = 2(x – 3) + 4x³ = 0

⇒ x = 1also (PQ²)¹¹ > 0 when x = 1

∴ The nearest point of Q(3, 2) is P(1, 3)

∴ Shortest distance = PQ = $\sqrt{5}$