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NDA 2025 Maths · Mathematics · Three Dimensional Geometry · hard

The point on the z-axis which is equidistant from (1,5,7) and (5,1,-4) is

Single correct option

The point on the zz-axis which is equidistant from (1,5,7)(1,5,7) and (5,1,−4)(5,1,-4) is
  1. A. (0,0,3)(0,0,3)
  2. B. (0,0,−32)(0,0,-\dfrac32)
  3. C. (0,0,32)\left(0,0,\dfrac32\right)
  4. D. (0,0,112)(0,0,\dfrac{11}{2})
Show answer and solution

Answer: (C) (0,0,32)\left(0,0,\dfrac32\right)

Let the point be (0,0,z)(0,0,z). Equating squared distances: 1+25+(z−7)2=25+1+(z+4)21+25+(z-7)^2=25+1+(z+4)^2, so (z−7)2=(z+4)2(z-7)^2=(z+4)^2, giving −14z+49=8z+16-14z+49=8z+16 and z=32z=\frac32. The option 112\frac{11}2 comes from adding 77 and 44 and halving, and the point (0,0,3)(0,0,3) doubles the correct value.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake