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NDA2017MathematicsThree Dimensional GeometryActual

A variable plane passes through a fixed point (a, b, c) and cuts the axes in A , B and C respectively. The locus of the centre of the sphere OABC , O being the origin, is

Options

  1. Ax a + y b + z c =1
  2. Ba x + b y + c z =1
  3. Ca x + b y + c z =2
  4. Dx a + y b + z c =2

Correct answer

C. a x + b y + c z =2

Step-by-step solution

Equation of plane passing through points (p, 0,0),(0, q, 0) and (0,0, r) is x p + y q + z r =1 Given that this plane passes through (a, b, c) . a p + b q + c r =1 Equation of sphere is x^2+y^2+z^2-p x-q y-r z=0 . Centre of the sphere =(1, m, n)= ( p 2 , q 2 , r 2 ) p =2 , q =2 ~m , r =2 n locus of the centre a x + b y + c z =2 .

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