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NDA 2 2024 Maths, question 65

Topic: Analytical geometry

Passage · Q65 to Q66

Let 2x2+2y2+2z2+3x+3y+3z−6=02x^{2}+2y^{2}+2z^{2}+3x+3y+3z-6=0 be a sphere.

Q65

What is the diameter of the sphere?

  1. (a) 534\frac{5\sqrt{3}}{4}
  2. (b) 532\frac{5\sqrt{3}}{2}Correct answer
  3. (c) 354\frac{3\sqrt{5}}{4}
  4. (d) 352\frac{3\sqrt{5}}{2}

Solution.

Answer: (b) 532\frac{5\sqrt{3}}{2}

  1. Divide by 2 and complete all three squares: (x+3/4)²+(y+3/4)²+(z+3/4)²=75/16.
  2. Thus r=5√3/4, and the diameter is 5√3/2.