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A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular to it from the origin is the sphere
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[a] Let (a, b, c) be the fixed point on the variable plane Now D. R?s of OM are x−0,y−0,z−0 i.e x, y, z D.R.?s of MA are x-a, y-b, z-c. Since OM perpendicular Ma x(x−a)+y(y−b)+z(z−c)=0 ⇒x2+y2+z2−ax−by−cx=0
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Question Text | A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular to it from the origin is the sphere |
Answer Type | Text solution:1 |
Upvotes | 150 |