Home
Class 12
MATHS
If the pair of lines ax^(2) + 2hxy + by...

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

A

`2fgh = bg^(2)+ ch^(2)`

B

`bg^(2) != ch^(2)`

C

abc = 2fgh

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|53 Videos

  • STATISTICS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|40 Videos

  • THREE DIMENSIONAL GEOMETRY

    NEW JOYTHI PUBLICATION|Exercise Objective|36 Videos

Similar Questions

Explore conceptually related problems

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If ax^(2) +2hxy + by^(2) + 2gx + 2fy + c = 0, find dy/dx.

If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k =

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

If the pairs of straight lines x^(2) - 2pxy-y^(2)=0 and x^(2) – 2qxy - y^(2) = 0 be such that each pair bisects the angle between the other pair, then

The set of lines ax + by + c = 0 where 3a + 2b + 4c = 0 intersect at the point

The equation x^(2) + y^(2) + 2gx + 2fy + c=0 reprsents the circle if

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=0

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0 .

If the pair of straight lines ax^(2)-2pxy-y^(2)=0and x^(2)-2qxy-y^(2)=0 are such that each pair bisects the angle between the other pair , then prove that pq=-1 .

NEW JOYTHI PUBLICATION-STRAIGHT LINES-QUESTIONS FROM COMPETITIVE EXAMS
  1. A straight line perpendicular to the 2x + y = 3 is passing through (1...

    Text Solution

    |

  2. If x sin ^3 theta +y cos^3 theta = sin theta cos theta and x sin ...

    Text Solution

    |

  3. If the pair of lines ax^(2) + 2hxy + by^(2)+ 2gx + 2fy + c = 0 int...

    Text Solution

    |

  4. The point of lines represented by 3ax^(2) + 5xy + (a^(2) – 2)y^(2) = ...

    Text Solution

    |

  5. Locus of midpoint of the portion between the axes of x cos alpha + y ...

    Text Solution

    |

  6. A triangle with vertices (4, 0), (-1, -1), (3, 5) is

    Text Solution

    |

  7. A square of side a lies above the x-axis and has one vertex at the or...

    Text Solution

    |

  8. If the pairs of straight lines x^(2) - 2pxy-y^(2)=0 and x^(2) – 2qxy ...

    Text Solution

    |

  9. Locus of centroid of the triangle whose vertices are (a cost, a sint)...

    Text Solution

    |

  10. Show that the area of the triangle formed by the lines y = m(1) x + c(...

    Text Solution

    |

  11. Let A (2, -3) and B (-2, 1) be vertices of a triangle ABC. If the cen...

    Text Solution

    |

  12. The equation of the straight line passing through the point (4, 3) an...

    Text Solution

    |

  13. If the sum of the slopes of the lines given by x^(2) – 2cxy – 7y^(2) ...

    Text Solution

    |

  14. If one of the lines given by 6x^(2) - xy + 4cy^(2) = 0 is 3x + 4y = 0...

    Text Solution

    |

  15. The line parallel to the x-axis and passing through the intersection ...

    Text Solution

    |

  16. If non-zero numbers a, b, c are in H.P., then the straight line (x)/(...

    Text Solution

    |

  17. If a vertex of a triangle is (1, 1) and the mid points of two sides t...

    Text Solution

    |

  18. If the pair of lines ax^(2) + 2(a+b)xy + by^(2) = 0 lie along diamete...

    Text Solution

    |

  19. A straight line through the point A(3, 4) is such that its intercept ...

    Text Solution

    |

  20. In are ellispe , the distance between its foci is 6 and its minor axi...

    Text Solution

    |