NCERT Class 12 · Ch 6 Exercise 6.3 · Q27
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 27
Which listed point on x²=2y is nearest (0,5)?
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: A: (2√2,4). The equally near point (−2√2,4) is absent from the options.
- Minimize squared distance D²=x²+(x²/2−5)²=x⁴/4−4x²+25.
- Its derivative is x(x²−8), giving x=0,±2√2. The squared distances are 25 and 9, respectively.
- The function tends to infinity as |x|→∞, so both (±2√2,4) are global nearest points. Only the positive one appears in the choices.
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