Home
Class 11
MATHS
If two curves, whose equations are ax^2+...

If two curves, whose equations are `ax^2+2hxy+by^2+2gx+2fy+c=0` and `a'x^2+2h'xy+b'y^2+2g'x+2f'y+c'=0` intersect in four concyclic points, prove that
`(a-b)/h=(a'-b')/(h')`

Promotional Banner

Topper's Solved these Questions

  • CARTESIAN COORDINATES AND STRAIGHT LINE

    PATHFINDER|Exercise QUESTION BANK|249 Videos

  • COMPLEX NUMBER

    PATHFINDER|Exercise QUESTION BANK|224 Videos

Similar Questions

Explore conceptually related problems

If the curves ax^2+4xy+2y^2+x+y+5=0 and ax^2+6xy+5y^2+2x+3y+8=0 intersect at four concyclic points then the value of a is

If two cricles x^2 + y^2 + 2gx + 2fy = 0 and x^2 +y^2 + 2g'x + 2f'y = 0 touch each other, then

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent

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

If the circles x ^(2) +y^(2) +2gx +2fy =0 and x ^(2) +y^(2) +2g'x+ 2f'y=0 touch each other then-

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

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

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2

Show that the two circles x^(2) + y^(2) + 2gx + 2fy = 0 and x^(2) + y^(2) + 2g'x+ 2f'y = 0 will touch each other if f'g = g'f.

The circles whose equations are x^2+y^2+c^2=2ax and x^2+y^2+c^2-2by=0 will touch one another externally, if :

PATHFINDER-CIRCLE-QUESTION BANK
  1. Show that the common tangents to the circles x^2+y^2-6x=0 and x^2+y^2+...

    Text Solution

    |

  2. Two straight lines rotate about two fixed points. If they start from t...

    Text Solution

    |

  3. If two curves, whose equations are ax^2+2hxy+by^2+2gx+2fy+c=0 and a'x^...

    Text Solution

    |

  4. Find the equation of the circle of minimum radius which contains the t...

    Text Solution

    |

  5. The number of common tangents to the circles x^2+y^2-4x-6y-12=0 and x^...

    Text Solution

    |

  6. A circle S passes through the point (0, 1) and is orthogonal to the ci...

    Text Solution

    |

  7. Let C be the circle with centre at (1, 1) and radius = 1. If T is the ...

    Text Solution

    |

  8. The circle passing through (1, - 2) and touching the axis of x at (3, ...

    Text Solution

    |

  9. A point P lines on the circle x^2+y^2=169. If Q = (5, 12) and R= (-12,...

    Text Solution

    |

  10. A circle passing through (0, 0), (2, 6), (6, 2) cuts the x-axis at the...

    Text Solution

    |

  11. A point moves so that the sum of squares of its distances from the poi...

    Text Solution

    |

  12. If one end of a diameter of the circle x^2+y^2-4x-6y+11=0 is (3, 4) th...

    Text Solution

    |

  13. The equation of the circle passing through the point (1, 1) and the po...

    Text Solution

    |

  14. The equations of the circles which touch both the axes and the line 4x...

    Text Solution

    |

  15. A tangent PT is drawn to the circle x^2+y^2 =4 at the point P(sqrt3,1)...

    Text Solution

    |

  16. A tangent PT is drawn to the circle x^2+y^2 =4 at the point P(sqrt3,1)...

    Text Solution

    |

  17. The length of the diameter of the circle which touches the x-axis at t...

    Text Solution

    |

  18. If the circles x^2 + y^2 + 2x + 2ky + 6 = 0 and x^2 + y^2 + 2ky + k = ...

    Text Solution

    |

  19. Four distinct points (2k,3k),(1,0),(0,1)and(0,0) lie on a circle for

    Text Solution

    |

  20. The incentre of an equilateral triangle is ( 1, 1) and the equation of...

    Text Solution

    |