Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The point(s) on the curve y 2 = 4x which is (are) closest to the curve x 2 + y 2 – 24y + 128 = 0 is (are)-
A
(0, 0)
B
(4, 4)
C
(2, 2 
)
)
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Let the point on parabola be (t 2 , 2t)
centre of circle ≡ (0, 12)
line through these points must be line of least length
d 2 = (t 2 – 0) 2 + (2t –12) 2 Let if f(t) = t
4 + 4 (t –6) 2 f ′ (t) = 4t
3 + 8(t – 6) = 4[t 3 + 2t –12]
= 0 for t = 2
Hence point ≡ (4, 4)
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems