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A variable plane is at a constant distan...

A variable plane is at a constant distance p from the origin and meets the axes at A,B,C. Through A,B,C plane are drawn parallel to the co-ordinate planes. Show that the locus of their points of intersection is `1/x^2+1/y^2+1/z^2=1/p^2`.

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Odisha Bureau.s Textbooks Solutions (Exercise 13(b)) (True (T) or False (F))
  1. In each of the following case, verift whether the four given points ar...

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  2. In each of the following case, verift whether the four given points ar...

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  3. In each of the following case, verift whether the four given points ar...

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  4. Find the equation of the plane Passing through the intersection of pla...

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  5. Find the equation of the plane Which contains the line of intersection...

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  6. Find the equation of the plane Passing through the intersection of ax...

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  7. Find the equation of the plane Passing through the intersection of the...

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  8. Find the angle between the following pairs of planes. x+3y-5z+1=0 and...

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  9. Find the angle between the following pairs of planes. x+2y+2z-3=0 and ...

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  10. Find the angle between the following pairs of planes. x+2y+2z-7=0 and ...

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  11. Find the equation of the bisector of the angles between the following...

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  12. Find the equation of the bisector of the angles between the following...

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  13. Show that the origin lies in the interior of the acute angle between p...

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  14. Prove that the line joining (1,2,3),(2,1,-1) intersects the line joini...

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  15. Show that the point (-frac{1}{2},2,0) is the circumcentre of the trian...

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  16. Show that plane ax+by+cz+d=0 divides the line segment joining (x1,y1,z...

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  17. A variable plane is at a constant distance p from the origin and meets...

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  18. A variable plane passes through a fixed point (a,b,c) and meets the co...

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  19. The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...

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  20. The plane lx+my=0 is rotated about its line of intersection with the p...

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