Mathematics · Three Dimensional Geometry
The distance from a point (1, 1, 1) to a variable plane π is 12 units and the points of intersection of the plane π with the X, Y, Z-axes are A, B, C respectively. If the point of intersection of the planes through the points A, B, C and parallel to the coordinate planes is P, then the equation of the locus of P is
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- 1(1xy + 1yz + 1zx) = 143(1x2 + 1y2 + 1z2)
- 21x2 + 1y2 + 1z2 = 144
- 3(1x + 1y + 1z - 1)2 = 144(1x2 + 1y2 + 1z2)✓
- 4(1x + 1y + 1z - 1)2 = 144(1x2 + 1y2 + 1z2)2
Correct answer
(1x + 1y + 1z - 1)2 = 144(1x2 + 1y2 + 1z2)
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