Home
Class 12
MATHS
Given that the two curves a r g(z)=pi/6a...

Given that the two curves `a r g(z)=pi/6a n d|z-2sqrt(3)i|=r` intersect in two distinct points, then `[r]!=2` b. `0

A

`[r] ne 2` where [.] represents greatest integer

B

`0 lt r lt 3`

C

`r = 6`

D

`3 lt r lt 2 sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, D

`CP=r,OC=2sqrt(3) , /_COP = pi//3`
`rArr Cp = OC sin .(pi)/(3)= 2sqrt(3)(sqrt(3))/(2) = 3`
Thus, when r=3, the cicle touches the line. Hencec, for two distinct points of intersection, `3ltrlt2sqrt(3)`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise MATRIX MATCH TYPE|9 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

The least value of p for which the two curves argz=(pi)/(6) and |z-2sqrt(3)i|=p intersect is

The two circles x^(2)+y^(2)=r^(2) and x^(2)+y^(2)-10x+16=0 intersect at two distinct points.Then

If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points , then

If the two circles (x+1)^(2)+(y-3)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct point,then (A)r>2(B)2

Statement-1:If the line y=x+c intersects the circle x^2+y^2=r^2 in two real distinct points then -rsqrt2 lt c lt r sqrt2 Statement -2: If two circles intersects at two distinct points then C_1C_2 lt r_1+r_2

Two circles with centres at C_(1) , C_(2) and having radii r_(1) , r_(2) will intersect each in two real distinct points if , and only if :

Statement I Circles x^(2)+y^(2)=4andx^(2)+y^(2)-6x+5=0 intersect each other at two distinct points Statement II Circles with centres C_(1),C_(2) and radii r_(1),r_(2) intersect at two distinct points if |C_(1)C_(2)|ltr_(1)+r_(2)

CENGAGE-COMPLEX NUMBERS-Exercise (Multiple)
  1. System of equaitons |z+3|-|z-3| = 6 and |z-4|=r where r in R^(+) has

    Text Solution

    |

  2. Let the equaiton of a ray be |z-2|-|z-1-i| = sqrt(2). If the is stri...

    Text Solution

    |

  3. Given that the two curves a r g(z)=pi/6a n d|z-2sqrt(3)i|=r intersect ...

    Text Solution

    |

  4. On the Argand plane ,let z(1) = - 2+ 3z,z(2)= - 2-3z and |z| = 1. T...

    Text Solution

    |

  5. Let S = { z: x = x+ iy, y ge 0,|z-z(0)| le 1}, where |z(0)|= |z(0) - o...

    Text Solution

    |

  6. If P andn Q are represented by the complex numbers z(1) and z(2) such...

    Text Solution

    |

  7. Loucus of complex number satifying are arg[(z-5+4i)//(z+3-2i)] = - pi...

    Text Solution

    |

  8. Equation of tangent drawn to circle |z| = r at the point A(z0), is

    Text Solution

    |

  9. If n is a natural number gt 2, such that z^(n) = (z+1)^(n), then

    Text Solution

    |

  10. If |z-(1//z)=1,t h e n (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(sqr...

    Text Solution

    |

  11. If 1,z(1),z(2),z(3),…….,z(n-1) be the nth roots of unity and omega b...

    Text Solution

    |

  12. Let z be a complex number satisfying equation z^p-z^(-q),w h e r ep ,q...

    Text Solution

    |

  13. Which of the following is ture ?

    Text Solution

    |

  14. If from a point P representing the complex number z1 on the curve |z...

    Text Solution

    |

  15. A complex number z is rotated in anticlockwise direction by an angle ...

    Text Solution

    |

  16. z(1),z(2),z(3) and z(1),z(2),z(3) are nonzero complex numbers such th...

    Text Solution

    |

  17. Given z=f(x)+ig(x)w h e r ef,g:(0,1)vec(0,1) are real valued functions...

    Text Solution

    |

  18. Let a, b, c be distinct complex numbers with |a|=|b|=|c|=1 and z(1), z...

    Text Solution

    |

  19. If a,b,c,d in R and all the three roots of az^3 + bz^2 + cZ + d=0 ha...

    Text Solution

    |

  20. If (3)/(2+e^(itheta)) =ax + iby, then the locous of P(x,y) will repre...

    Text Solution

    |