Home
Class 11
MATHS
If z(1) and z(2) are two fixed points in...

If `z_(1) and z_(2)` are two fixed points in the Argand plane, then find the locus of a point z in each of the following
`|z-z_(1)|-|z-z_(2)|=` constant `(ne |z_(1)-z_(2)|)`

Text Solution

Verified by Experts

The correct Answer is:
P lies on a hyperbola having its foci at A and B respectively
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (A)|27 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (B)|69 Videos

  • COMPLEX NUMBER

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |34 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

Similar Questions

Explore conceptually related problems

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| - |z-z_(2)|= |z_(1)-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

Let z_(1) and z_(2) be two given complex numbers. The locus of z such that {:("Column -I", " Column -II"),( "(A) " |z-z_(1)|+|z-z_(2)| = " constant =k, where " k ne|z_(1)-z_(2)|, " (p) Circle with " z_(1) and z_(2) " as the vertices of diameter"),("(B)" |z-z_(1)|- |z-z_(2)|= " k where " k ne |z_(1)-z_(2)| ," (q) Circle "),("(C)"arg((z-z_(1))/(z-z_(2)))=+- pi/2 , " (r) Hyperbola "),("(D) If "omega" lies on " |omega| = 1 " then " , " (s) Ellipse"):}

locus of the point z satisfying the equation |z-1|+|z-i|=2 is

If A(z_(1)) and B(z_(2)) are two points in the Argand plane such that z_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0 , then triangleOAB , is

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then prove that z_1, z_2, z_3, z_4 are concyclic.

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

Statement-1: If z_(1),z_(2) are affixes of two fixed points A and B in the Argand plane and P(z) is a variable point such that "arg" (z-z_(1))/(z-z_(2))=pi/2 , then the locus of z is a circle having z_(1) and z_(2) as the end-points of a diameter. Statement-2 : arg (z_(2)-z_(1))/(z_(1)-z) = angleAPB

If A(z_(1)),B(z_(2)) and C(z_(3)) are three points in the Argand plane such that z_(1)+omegaz_(2)+omega^(2)z_(3)=0 , then

ICSE-COMPLEX NUMBERS-Chapter Test
  1. If z(1) and z(2) are two fixed points in the Argand plane, then find t...

    Text Solution

    |

  2. Find the square root of 5-12i

    Text Solution

    |

  3. Find the locus of a complex number z=x +yi, satisfying the relation |z...

    Text Solution

    |

  4. Express (13i)/(2-3i) in the form A + Bi

    Text Solution

    |

  5. If z= x +yi and (|z-1-i|+4)/(3|z-1-i|-2)=1, show that x^(2) + y^(2) -2...

    Text Solution

    |

  6. If omega and omega^(2) are cube roots of unity, prove that (2- omega +...

    Text Solution

    |

  7. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

    Text Solution

    |

  8. If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of ...

    Text Solution

    |

  9. Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

    Text Solution

    |

  10. Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

    Text Solution

    |

  11. Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + i...

    Text Solution

    |

  12. Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

    Text Solution

    |

  13. Find the locus of a complex number z= x + yi, satisfying the relation ...

    Text Solution

    |

  14. Find the real values of x and y satisfying the equality (x-2 + (y-3)i)...

    Text Solution

    |

  15. If i= (sqrt-1), prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)...

    Text Solution

    |

  16. If z= x + yi and |2z + 1| = |z- 2i|, show that 3(x^(2) + y^(2)) + 4(x-...

    Text Solution

    |

  17. Find the amplitude of the complex number "sin" (6pi)/(5) + i (1- "cos"...

    Text Solution

    |

  18. Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

    Text Solution

    |

  19. Find the value of x and y given that (x + yi) (2-3i)=4+i

    Text Solution

    |

  20. If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z l...

    Text Solution

    |

  21. If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and...

    Text Solution

    |