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Co - ordinate Geometry 3D Geometry

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A variable plane passes through a fixed point (a, b, c) and meets the coordinate axis in A, B, C. The locus of midpoint of the plane common through A, B, C and parallel to the coordinate planes is

A. ax + by + cz = 1

B. ax^–1+ by^–1+ cz^–1 = 1

C. ax^–2 + by^–2 + cz^–2 = 1

D. ax + by + cz = -1

E. None of the above

View Answer

Correct choice: B

Explanation:

Let the equation of plane be x/α + y/β + z/γ = 1
Where OA = α. OB = β and OC = γ
Since (1) passes through (a, b, c)
∴ a/α + b/β + c/γ = 1 ……………(2)
The equation of the plane through A(α, 0, 0) and parallel to yz plane is x= α. The equation of the plane passing through B(0, β, 0) and parallel to xz plane is y = β. The equation of the plane through C(0, 0, γ) and parallel to xy plane is z = γ
∴ Coordinate of the common point to the plane is (α, β, γ)
We have to find locus of α, β, γ which can be obtained by replacing (α, β, γ) by (x, y, z) in (2)

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Eamcet Mathematics Co - ordinate Geometry 3D Geometry

Eamcet Mathematics
Co - ordinate Geometry 3D Geometry