Home
Class 12
MATHS
The extremities of a diameter of a sp...

The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos
  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

Three solid spheres of iron whose diameters are 2cm, 12cm and 16cm, respectively, are melted into a single solid sphere. Find the radius of the solid sphere.

Three solid spheres of iron whose diameters are 2cm, 12cm and 16cm, respectively, are melted into a single solid sphere. Find the radius of the solid sphere.

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Find the equation of the sphere described on the joint of points Aa n dB having position vectors 2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k , respectively, as the diameter. Find the center and the radius of the sphere.

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Metallic spheres of diameters 12 cm, 16 cm and 20 cm respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

The plane x/a+y/b+z/c=1 meets the coordinate axes at A,B and C respectively. Find the equation of the sphere OABC.

The plane x/a+y/b+z/c=1 meets the coordinate axes at A,B and C respectively. Find the equation of the sphere OABC.

The height and radius of base of a metallic cone are 27 cm and 16 cm respectively .It is melted and recast into a sphere .Find the radius and curved surface of the sphere.

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the pla...

    Text Solution

    |

  2. Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and t...

    Text Solution

    |

  3. The extremities of a diameter of a sphere lie on the positive y- an...

    Text Solution

    |

  4. A plane passes through a fixed point (a ,b ,c)dot Show that the loc...

    Text Solution

    |

  5. Find the radius of the circular section of the sphere | vec r|=5 by...

    Text Solution

    |

  6. A point P(x ,y ,z) is such that 3P A=2P B , where Aa n dB are the p...

    Text Solution

    |

  7. Find the shortest distance between lines vec r=( hat i+2 hat j+ hat...

    Text Solution

    |

  8. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4a ...

    Text Solution

    |

  9. Determine whether the following pair of lines intersect or not. (1...

    Text Solution

    |

  10. Find the equation of plane which is at a distance 4/(sqrt(14)) from...

    Text Solution

    |

  11. Find the unit vector perpendicular to the plane vec rdot(2 hat i+ ...

    Text Solution

    |

  12. If the straight lines x=-1+s ,y=3-lambdas ,z=1+lambdasa n dx=t/2,y=1+t...

    Text Solution

    |

  13. Find the equation of a line which passes through the point (1,1,1) ...

    Text Solution

    |

  14. Find the vector equation of a line passing through 3 hat i-5 hat j+7...

    Text Solution

    |

  15. Find the equation of the plane passing through the point (2,3,1) ha...

    Text Solution

    |

  16. Find the equation of the plane through the points (2, 3, 1) and (4, -5...

    Text Solution

    |

  17. Find the equation of the image of the plane x-2y+2z-3=0 in plane x+...

    Text Solution

    |

  18. Find the equation of a plane which passes through the point (1, 2, 3) ...

    Text Solution

    |

  19. Find the equation of a plane which is parallel to the plane x-2y+2z=5 ...

    Text Solution

    |

  20. Find the direction ratios of orthogonal projection of line (x-1)/(1)=(...

    Text Solution

    |