Home
Class 11
MATHS
If the pair of lines ax^(2)+2hxy+by^(2)+...

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)`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 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 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 equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pair of parallel lines, prove that a/h = h/b = g/f

Find the derivatives w.r.t. x : ax^(2)+2hxy+by^(2)+2gx+2fy+c=0

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

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

If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pair of parallel lines, prove that The distance between them is 2sqrt((g^2 - ac)/(a(a + b)))

The gradient of one of the lines ax^2+2hxy+by^2=0 is twice that of the other, then

If one of the pair of lines ax^2+2hxy+by^2=0 bisects the angle between coordinate axes in positive quadrant, then

If one of the lines denoted by the line pair a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes, then prove that (a+b)^2=4h^2

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

    Text Solution

    |

  2. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

    Text Solution

    |

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

    Text Solution

    |

  4. A circle passes through the origin and has its center on y=x If it cut...

    Text Solution

    |

  5. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

    Text Solution

    |

  6. The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle ...

    Text Solution

    |

  7. If S(1)=alpha^(2)+beta^(2)-a^(2), then angle between the tangents from...

    Text Solution

    |

  8. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

    Text Solution

    |

  9. Find the angle between the two tangents from the origin to the circle ...

    Text Solution

    |

  10. Two circles C1 and C2 intersect at two distinct points PandQ in a line...

    Text Solution

    |

  11. Find the equation of the tangent at the endpoints of the diameter of ...

    Text Solution

    |

  12. Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 whic...

    Text Solution

    |

  13. If from any point P on the circle x^2+y^2+2gx+2fy+c=0, tangents are dr...

    Text Solution

    |

  14. The lengths of the tangents from P(1,-1) and Q(3,3) to a circle are sq...

    Text Solution

    |

  15. Which of the following is a point on the common chord of the circle x^...

    Text Solution

    |

  16. If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersec...

    Text Solution

    |

  17. The circles x^2+y^2+x+y=0and x^2+y^2+x-y=0intersect at an angle of

    Text Solution

    |

  18. The common chord of x^2+y^2-4x-4y=0 and x^2+y^2=16 subtends at the ori...

    Text Solution

    |

  19. If the tangents are drawn to the circle x^2+y^2=12 at the point where ...

    Text Solution

    |

  20. If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the cir...

    Text Solution

    |