Home
Class 11
MATHS
Let z=1-t+isqrt(t^2+t+2), where t is rea...

Let `z=1-t+isqrt(t^2+t+2)`, where t is real parameter. The locus of z in the argand plane is

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

Let z=t^2-1+sqrt(t^4-t^2),where t in R is a parameter. Find the locus of z depending upon t , and draw the locus of z in the Argand plane.

If t is parameter then the locus of the point P(t,(1)/(2t)) is _

Let A(z_(1)) and B(z_(2)) are two distinct non-real complex numbers in the argand plane such that (z_(1))/(z_(2))+(barz_(1))/(z_(2))=2 . The value of |/_ABO| is

The coordinates of a moving point P are (at^(2),2at) , where t is a variable parameter . Find the equation to the locus of P.

Show that equations x = 5 * (1 - t^(2))/(1 + t^(2)), y = 6 * (t)/(1 + t^(2) ) where t is a variable parameter, define an ellipse . Find its eccentricity .

Prove that the equations x = 6 (cosec t + sin t ) and y = 15(cosec t - sin t ) where t is a variable parameter, represent a hyperbola.

Position vector of a particle is related to time t as vecr=(t^2-1)hati+2thatj . The locus of the particle on the x-y plane is

The coordinates of moving point P are ((2t+1)/(3t-2),(t-1)/(t+1)) , where t is a variable parameter . Find the equation to the locus of P.

If x=t+(1/t), y=t-(1/t) and t=parameter then the locus of the point (x, y) is __

The coordinates of a moving point P are (ct+(c)/(t),ct-(c)/(T)) , where t is a variable parameter . Find the equation to the locus of P.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |

  2. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  3. Let z=1-t+isqrt(t^2+t+2), where t is real parameter. The locus of z in...

    Text Solution

    |

  4. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

    Text Solution

    |

  5. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

    Text Solution

    |

  6. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

    Text Solution

    |

  7. z^2+zabsz+absz^2=0 then the locus of z is

    Text Solution

    |

  8. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

    Text Solution

    |

  9. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  10. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |

  11. z1a n dz2 lie on a circle with center at the origin. The point of inte...

    Text Solution

    |

  12. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

    Text Solution

    |

  13. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

    Text Solution

    |

  14. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

    Text Solution

    |

  15. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

    Text Solution

    |

  16. Find a quadratic equation whose product of roots x1 and x2 is equa...

    Text Solution

    |

  17. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

    Text Solution

    |

  18. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

    Text Solution

    |

  19. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

    Text Solution

    |

  20. Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C ...

    Text Solution

    |