Home
Class 12
MATHS
Find the equation of the sphere passin...

Find the equation of the sphere passing through `(0,0,0),(1,0,0),(0,1,0) and (0,0,1)dot`

Text Solution

Verified by Experts

Let the equation of the sphere be
`" "x^(2)+y^(2)+z^(2)+2ux+2vy+2wx=0" "`(i)
As (i) passes through (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1), we must have `d=0, 1+2u+d=0`
`1+2v+d=0 and 1+2w+d=0`
Since `d=0`, we get `2u=2v=2w=-1`
Thus, the equation of the required sphere is `x^(2)+y^(2)+z^(2)-x-y-z=0`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the sphere which passes through (1,0,0),(0,1,0) and (0,0,1) and whose centre lies on the plane 3x-y+z=2.

find the equation of the sphere passing through the four points (0,0,0), (1,0,0), (0,1,0) and (0,0,1)

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) .

Find the equation of a sphere which passes through (1,0,0)(0,1,0)a n d(0,0,1), and has radius as small as possible.

Find the equation of the plane passing through A(2,2,-1),B(3,4, 2)a n dC(7,0,6)dot

Find the equation of the line passing through the points (1,2,3)a n d(-1,0,4)dot

Find the equation of the plane passing through the points (3,4,1) and (0,1,0) and parallel to the line (x+3)/(2)=(y-3)/(7)=(z-2)/(5) .

Find the equation of each of the circles passing through the points : (0, 0), (1, 2), (2, 0)

The equation of the circle passes through the point (0, 4), (0, 0) and (3, 0) is

Find the radius of the circle passing through (6,0), (0,8) and origin .