Home
Class 11
MATHS
The line A x+B y+C=0 cuts the circle x^2...

The line `A x+B y+C=0` cuts the circle `x^2+y^2+a x+b y+c=0` at `Pa n dQ` . The line `A^(prime)x+B^(prime)x+C^(prime)=0` cuts the circle `x^2+y^2+a^(prime)x+b^(prime)y+c^(prime)=0` at `Ra n dSdot` If `P ,Q ,R ,` and `S` are concyclic, then show that `|a-a ' b-b ' c-c ' A B C A ' B ' C '|=0`

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 circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

Find the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d ' are perpendicular.

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , then find the equation of the circle on A B as diameter.

If the chord of contact of tangents from a point on the circle x^(2) + y^(2) = a^(2) to the circle x^(2)+ y^(2)= b^(2) touches the circle x^(2) + y^(2) = c^(2) , then a, b, c are in-

The equations of tangents to the circle x^2+y^2-6x-6y+9=0 drawn from the origin in (a). x=0 (b) x=y (c) y=0 (d) x+y=0

If x/(b +c) = y/(c+a) = z/(a + b) , then show that a/(y+z-x) = b/(z+x - y) = c/(x + y - z) .

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime) =0 has perpendicular diagonals, then (a) b^2+c^2=b^('2)+c^('2) (b) c^2+a^2=c^('2)+a^('2) (c) a^2+b^2=a^('2)+b^('2) (d) none of these

If x^2+y^2=1, then (a) y y^('')-2(y^(prime))^2+1=0 (b) yy^('')+(y^(prime))^2+1=0 (c) y y^('')+(y^(prime))^(-2)-1=0 (d) y y^('')+2(y^(prime))^2+1=0

If x/(b + c -a) = y/(c + a - b) = z/(a + b -c) , then show that (b -c) x + (c-a) y + (a -b) z = 0 .

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. An infinite number of tangents can be drawn from (1,2) to the circle x...

    Text Solution

    |

  2. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

    Text Solution

    |

  3. The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . ...

    Text Solution

    |

  4. Find the equation of the circle which cuts the three circles x^2+y^2-3...

    Text Solution

    |

  5. Equation of a circle with centre (4, 3) touching the circle x^2+y^2=1 ...

    Text Solution

    |

  6. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

    Text Solution

    |

  7. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |