Home
Class 12
MATHS
Identify the locus of z if z = a +(r^...

Identify the locus of `z` if ` z = a +(r^2)/(z-a),> 0.`

Text Solution

AI Generated Solution

To solve the problem of identifying the locus of \( z \) given the equation \[ z = a + \frac{r^2}{z - a}, \quad r > 0, \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

Identify the locus of z if bar z = bar a +(r^2)/(z-a).

Identify locus z if R e(z+1)=|z-1|

Find the locus of z if arg ((z-1)/(z+1))= pi/4

The locus of point z satisfying Re (z^(2))=0 , is

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z in Rdot

In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2z^2-5z+3)/(2z^2-z-2))}=(2pi)/3dot

In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2z^2-5z+3)/(3z^2-z-2))}=(2pi)/3dot

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If |z1-1|lt=,|z2-2|lt=2,|z(33)|lt=3, then find the greatest value of |...

    Text Solution

    |

  2. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

    Text Solution

    |

  3. Identify the locus of z if z = a +(r^2)/(z-a),> 0.

    Text Solution

    |

  4. If z is any complex number such that |3z-2|+|3z+2|=4 , then identify t...

    Text Solution

    |

  5. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

    Text Solution

    |

  6. Let z be a complex number having the argument theta ,0 < theta < pi/2,...

    Text Solution

    |

  7. How many solutions the system of equations ||z + 4 |-|z-3i|| =5 and...

    Text Solution

    |

  8. Prove that |Z-Z1|^2+|Z-Z2|^2=a will represent a real circle [with cent...

    Text Solution

    |

  9. If |z-2-3i|^(2) + |z- 5 - 7i|^(2)= lambda respresents the equation ...

    Text Solution

    |

  10. If (|2z - 3|)/(|z-i|)= k is the equation of circle with complex numbe...

    Text Solution

    |

  11. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  12. If complex numbers z(1)z(2) and z(3) are such that |z(1)| = |z(2)| = |...

    Text Solution

    |

  13. If the triangle fromed by complex numbers z(1), z(2) and z(3) is eq...

    Text Solution

    |

  14. Show that the equation of a circle passings through the origin and...

    Text Solution

    |

  15. The triangle formed by A(z(1)), B(z(2)) and C(z(3)) has its circumc...

    Text Solution

    |

  16. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

    Text Solution

    |

  17. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, the...

    Text Solution

    |

  18. If z=z0+A( z -( z )0), w h e r eA is a constant, then prove that loc...

    Text Solution

    |

  19. z1a n dz2 are the roots of 3z^2+3z+b=0. if O(0),(z1),(z2) form an equi...

    Text Solution

    |

  20. Let z(1),z(2) and z(3) be three complex number such that |z(1)-1|= |z...

    Text Solution

    |