Home
Class 11
MATHS
If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0...

If `((3-z_1)/(2-z_1))((2-z_2)/(3-z_2))=k(k >0)` , then prove that points `A(z_1),B(z_2),C(3),a n dD(2)` (taken in clockwise sense) are concyclic.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If A(z_1),B(z_2),C(z_3) and D(z_4) be the vertices of the square ABCD then

If a r g["z"_1("z"_3-"z"_2)]=a r g["z"_3("z"_2-"z"_1)] , then prove that O ,z_1, z_2, z_3 are concyclic, where O is the origin.

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If z_1^2+z_2^2+2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

If z_1=2-i, z_2=1+i, find abs((z_1+z_2+1)/(z_1-z_2+i))

If z_(1)^(2)+z_(2)^(2)+z_(3)^(2)-z_(1)z_(3)-z_(1)z_(2)-z_(2)z_(3)=0" ""prove that" " "|z_(2)-z_(3)|=|z_(3)-z_(1)|=|z_(1)-z_(2)|, "where" " " z_(1),z_(2),z_(3) are complex numbers.

Let A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if

If |z_1-1|lt=1,|z_2-2|lt=2,|z_(3)-3|lt=3, then find the greatest value of |z_1+z_2+z_3|dot

If the fourth roots of unity are z_1,z_2,z_3,z_4 then z_1^2+z_2^2+z_3^2+z_4^2 is equal to

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

    Text Solution

    |

  2. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  3. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  4. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. ...

    Text Solution

    |

  5. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  6. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^...

    Text Solution

    |

  7. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

    Text Solution

    |

  8. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and...

    Text Solution

    |

  9. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

    Text Solution

    |

  10. If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are t...

    Text Solution

    |

  11. Find the real part of (1-i)^(-i)dot

    Text Solution

    |

  12. The equation (x^2+x+1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will h...

    Text Solution

    |

  13. Convert of the complex number in the polar form: 1-i

    Text Solution

    |

  14. If alpha,beta are the roots of a x^2+c=b x , then the equation (a+c y)...

    Text Solution

    |

  15. If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)

    Text Solution

    |

  16. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

    Text Solution

    |

  17. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

    Text Solution

    |

  18. If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of r...

    Text Solution

    |

  19. Find real value of x and y for which the complex numbers -3+i x^2y ...

    Text Solution

    |

  20. Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x...

    Text Solution

    |