Home
Class 12
MATHS
The line Ax+By+=0 cuts the circle by x^2...

The line Ax+By+=0 cuts the circle by `x^2+y^2+Ax+By+C=0`at P and Q. The line A'x +B'x+C'=0 cuts the circle `x^2+y^2+a'x+b'y+c'=0` at R and S.If P,Q, R and S are concyclic then show that `det (( a-a", b-b',c-c'),(A,B,C),(A',B',C'))=0`

Promotional Banner

Topper's Solved these Questions

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

Similar Questions

Explore conceptually related problems

The line ax+by+c=0 is normal to the circle x^(2)+y^(2)+2gy+2fy+d=0, if

The line ax +by+c=0 is an normal to the circle x^(2)+y^(2)=r^(2) . The portion of the line ax +by +c=0 intercepted by this circle is of length

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot

If the lines 5x+3y-15=0 and 3x+5y-15=0 cut both the axes at A,B,C and D then

Line x/a+y/b=1 cuts the coordinate axes at A(a,0) and B(0,0) and the line x/a+y/b= -1 at A'(-a',0) and B'(0,-b') . If the points A,B A' ,B' are concyclic , then the orthocentre of the triangle ABA' is

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

If a, b, c in R and 2a + 3b + 6c = 0, then the equation ax^(2) + bx + c = 0 has

A DAS GUPTA-Circles-EXERCISE
  1. Find the equation of the circle passing through the point of intersect...

    Text Solution

    |

  2. Find the equation of the circle whose diameter is the common chord of ...

    Text Solution

    |

  3. The line Ax+By+=0 cuts the circle by x^2+y^2+Ax+By+C=0at P and Q. The ...

    Text Solution

    |

  4. Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the...

    Text Solution

    |

  5. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

    Text Solution

    |

  6. Consider a family of circles passing through two fixed points A (3,7) ...

    Text Solution

    |

  7. If the circle C1: x^2 + y^2 = 16 intersects another circle C2 of radiu...

    Text Solution

    |

  8. The equation of the circle passing through the origin & cutting the ci...

    Text Solution

    |

  9. The equation of the circle which passes through the origin, center lie...

    Text Solution

    |

  10. Prove that the two circles each of which passes through the point (0, ...

    Text Solution

    |

  11. If the equations of two circles, whose radii are r and R respectively,...

    Text Solution

    |

  12. The centre of the circle S=0 lies on the line 2x-2y+9=0 and it cuts th...

    Text Solution

    |

  13. The centre of the circle that cuts the circle x^2 +y^2 + 2g x + 2fy + ...

    Text Solution

    |

  14. Find the equation of a circle which is co-axial with circles 2x^2 + 2y...

    Text Solution

    |

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

    Text Solution

    |

  16. From a point P, tangents drawn to the circle x^2 + y^2 + x-3=0, 3x^2 +...

    Text Solution

    |

  17. Let A = (-2,0) and B = (1,0) and P is a variable point such that /APB ...

    Text Solution

    |

  18. A point moves such that the sum of the squares of its distances from t...

    Text Solution

    |

  19. Two rods of lengths aa n db slide along the x- and y-a xi s , respecti...

    Text Solution

    |

  20. A variable circle passes through the point P (1, 2) and touches the x-...

    Text Solution

    |