Home
Class 11
MATHS
Show that |(z-2)/(z-3)|=2 represents a c...

Show that `|(z-2)/(z-3)|=2` represents a circle. Find the centre of radius.

Text Solution

Verified by Experts

The correct Answer is:
`(2)/(3)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (Match Column & Short Questions)|15 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (Objective type questions)|16 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|11 Videos

  • BINOMIAL THEOREM

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|7 Videos

  • CONIC SECTIONS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|9 Videos

Similar Questions

Explore conceptually related problems

If |(z-2)/(z-3)|=2 represents a circle, then find its radius.

If |(z-2)/(z-3)|=2 express a circle, then its radius is ......

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

Find the equation of the circle with centre (-3,2) and radius 4 .

show that the set of all point satisfying |z-1|=|z-i| represents a line passing through origin with slope -1 .

In each of the following find the equation of the circle with centre (-2,3) and radius 4

In each of the following find the equation of the circle with centre (0,2) and radius 2

Obtain equation of circle in Centre (2,-3) and radius sqrt(2a) .

Obtain equation of circle in Centre (a,a) and radius sqrt(2a) .

Show that all the roots of the equation a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=3, (where|a_(i)|le1,i=1,2,3,4,) lie outside the circle with centre at origin and radius 2//3.

KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)
  1. If |z+1|=z+2(1+i) then find the value of z.

    Text Solution

    |

  2. If arg(z-1)=arg(z+3i), then find x-1,y, where z=x+iy

    Text Solution

    |

  3. Show that |(z-2)/(z-3)|=2 represents a circle. Find the centre of radi...

    Text Solution

    |

  4. If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value ...

    Text Solution

    |

  5. z(1) and z(2) are two complex number such that |z(1)|=|z(2)| and arg (...

    Text Solution

    |

  6. If |z(1)|=1(z(1) ne -1) and z(2)=(z(1)-1)/(z(1)+1) then show that the ...

    Text Solution

    |

  7. If z(1), z(2) and z(3), z(4) are two pairs of conjugate complex number...

    Text Solution

    |

  8. If |z(1)|=|z(2)|=....|z(n)|=1, then show that, |z(1)+z(2)+z(3)+....z(n...

    Text Solution

    |

  9. If the complex numbers z(1) and z(2) arg (z(1))- arg(z(2))=0 then show...

    Text Solution

    |

  10. Solve the system of equation Re(z^(2))=0,|z|=2.

    Text Solution

    |

  11. Find the complex number satsifying the equation z+sqrt(2)|(z+1)|+i=0

    Text Solution

    |

  12. Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the pola...

    Text Solution

    |

  13. If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)...

    Text Solution

    |

  14. Fill in the blanks of the following For any two complex numbers z(1)...

    Text Solution

    |

  15. Fill in the blanks of the following the value of sqrt(-25)xxsqrt(-9)...

    Text Solution

    |

  16. Fill in the blanks of the following The number ((1-i)^(2))/(1-i^(3))...

    Text Solution

    |

  17. Fill in the blanks of the following The sum of the series i+i^(2)+i^...

    Text Solution

    |

  18. Fill in the blanks of the following Multiplicative inverser of 1+I i...

    Text Solution

    |

  19. Fill in the blanks of the following If z(1) and z(2) are complex num...

    Text Solution

    |

  20. Fill in the blanks of the following arg(z)+ arg(barz) where (barz ne...

    Text Solution

    |