Home
Class 12
MATHS
The equation 12x^2-2y^2-6z^2-2xy-8xy+6xz...

The equation `12x^2-2y^2-6z^2-2xy-8xy+6xz=0` represents

A

a pair of straight lines

B

a pair of planes

C

a shere

D

a pair of planes not passing through the origin.

Text Solution

Verified by Experts

The correct Answer is:
B
The given equation can be factorized as
`(3x+y+3z)(4x-2y-2z)=0`
`implies3x+y+z=0` and `4x-2y-2z=0`
Clerarly, these two equations represents planes passing through the origin.
Promotional Banner

Topper's Solved these Questions

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|16 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|33 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

Similar Questions

Explore conceptually related problems

If the equation 12x^(2)+7xy-py^(2)-18x+qy+6=0 represents a pair of perpendicular straight lines, then

If the equation 12x^(2)+7xy-py^(2)-18x+qy+6=0 represents a pair of perpendicular straight lines, then

The equation 16x^(2)+y^(2) +8xy-74x-78y+212 =0 represents

The equation x^(2) + y^(2) - 2xy -1 =0 represents :

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

The equation 8x^2 +8xy +2y^2+26x +13y+15=0 represents a pair of straight lines. The distance between them is

The equation x^(3)-6x^(2)y+11xy^(2)-6y^(3)=0 represents three straight lines passing through the origin, the slopes of which form an

If the equation 3x^(2)+xy-y^(2)-3x+6y+k=0 represents a pair of straight lines, then the value of k, is

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

Prove that the equation 8x^2+8xy+2y^2+26x+13y+15=0 represents a pair of parallel straight lines . Also find the perpendicular distance between them .

OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section I - Solved Mcqs
  1. The plane 2x-(1+lambda)y+3lambdaz=0 passes through the intersection of...

    Text Solution

    |

  2. If a plane meets the coordinates axes at A, Band C, in such a way that...

    Text Solution

    |

  3. The equation 12x^2-2y^2-6z^2-2xy-8xy+6xz=0 represents

    Text Solution

    |

  4. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

    Text Solution

    |

  5. The line (x-2)/3=(y+1)/2=(z-1)/-1 intersects the curve x y=c^(2),z=0 i...

    Text Solution

    |

  6. A non-zero vectors a is parallel to the line of intersection of the pl...

    Text Solution

    |

  7. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

    Text Solution

    |

  8. Equations of the line passing through (1,1,1) and perpendicular to th...

    Text Solution

    |

  9. Find the line of intersection of the planes vecr.(3hati-hatj+hatk)=1 a...

    Text Solution

    |

  10. Given the line L: (x-1)/(3) = (y+1)/(2) = (z +3)/(1) and the plane pi...

    Text Solution

    |

  11. The equation of the plane containing the line vecr = hati + hatj + lam...

    Text Solution

    |

  12. The ratio in which the plane vecr.(veci-2 vecj+3veck)=17 divides the l...

    Text Solution

    |

  13. The sine of the angle between the line (x-2)/(3) = (y-3)/(4) = (z-4)/(...

    Text Solution

    |

  14. If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...

    Text Solution

    |

  15. Let the pairs veca, vecb and vecc vecd each determine a plane. Then th...

    Text Solution

    |

  16. The equation of the plane containing the lines vecr = vec a (1) + lam...

    Text Solution

    |

  17. The points A(2-x,2,2), B(2,2-y,2), C(2,2,2-z) and D(1,1,1) are coplana...

    Text Solution

    |

  18. Find the vector equation of the plane in which the lines vecr=hati+ha...

    Text Solution

    |

  19. The equation of the plane which contains the origin and the line of in...

    Text Solution

    |

  20. The length of the perpendicular from the origin to the plane passing t...

    Text Solution

    |