Question

The point(s) on the curve y² = 4x which is (are) closest to the curve x² + y² – 24y + 128 = 0 is (are)-

• A. (0, 0)
• B. (4, 4)
• C. (2, 2$\sqrt{2}$)
• D. None of these

Answer 1

Answer: (B)

(4, 4)

Answer 2

Let the point on parabola be (t², 2t)

centre of circle º (0, 12)

line through these points must be line of least length

d² = (t² – 0)² + (2t –12)²

Let if f(t) = t⁴ + 4 (t –6)²

f ¢(t) = 4t³ + 8(t – 6) = 4[t³ + 2t –12]

= 0 for t = 2

Hence point º (4, 4)