Home
Class 12
MATHS
If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+...

If `ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n')`, then prove that :
`|{:(a,h,g),(h,b,f),(g,f,c):}|=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Check your understanding|10 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Competition file|14 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

ax^2+2hxy+by^2+2gx+2fy+c=0

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two parallel straight lines, then

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents parallel straight lines, then

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis,then prove that 2fgh=bg^(2)+ch^(2)

If the angle between the two lines given by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (pi)/4 , then the contsntant a,b,h,g,f,c are related by

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 resents a pair of parallel lines then prove that

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis then

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 repersents a hyperbola if

If the straight lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the X -axis,then

MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  2. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

    Text Solution

    |

  3. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

    Text Solution

    |

  4. If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

    Text Solution

    |

  5. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

    Text Solution

    |

  6. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  7. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

    Text Solution

    |

  8. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

    Text Solution

    |

  9. If A=[1tanx-tanx1] , show that A^T\ A^(-1)=[cos2x-sin2xsin2xcos2x] .

    Text Solution

    |

  10. If A=[(2,-3),(4,6)] " verify that " (adj A)^(-1)=(adj A^(-1)).

    Text Solution

    |

  11. Prove that : adj. I(n)=I(n)

    Text Solution

    |

  12. Prove that : adj.O=O

    Text Solution

    |

  13. Prove that : I(n)^(-1)=I(n)

    Text Solution

    |

  14. Find the inverse of each of the matrices given below : Let D= "dia...

    Text Solution

    |

  15. Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}...

    Text Solution

    |

  16. Find the inverse of each of the matrices given below : Obtain the in...

    Text Solution

    |

  17. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

    Text Solution

    |

  18. If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of ...

    Text Solution

    |

  19. Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integ...

    Text Solution

    |

  20. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |