Home
Class 11
MATHS
If the line y =sqrt(3)x cuts the curve x...

If the line `y =sqrt(3)x` cuts the curve `x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=0` at the point `A , B , C ,` then `O AdotO BdotO C` is equal to `(k/(13))(3sqrt(3)-1)` . The value of `k` is______

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

if the line y=xsqrt3 cuts the curve x^3+y^3+3xy+5x^2+3y^2+4x+5y+1=0 at point A,B,C then find the value of OA.OB.OC is equal to (where O is the origin)

If the line y=x cuts the curve x^3+3y^3-30 x y+72 x-55=0 in points A ,Ba n dC(O is origin), then the value of (4sqrt(2))/(55)O AdotO BdotO C is

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0 at the origin intersect at an angle theta equal to (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If the circle 2x^(2) + 2y^(2) = 5x touches the line 3x + 4y = k , then the values of k are

The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points A and B . The circle on A B as diameter passes through the origin. Then the value of k^2 is__________

If the line (x-1)/(5)=(y-3)/(2)=(z-3)/(2) intersects the curve x^(2)-y^(2)=k^(2), z=0 , then the value of 2k can be equal to

If the area bounded by the curves {(x, y)|x^(2)-y+1 ge 0} and {(x, y)|x+y-3 ge0} is k square units, then the value of 3k is equal to

If the lines 2x + y -3 = 0 , 5x + k y - 3 = 0 and 3x - y - 2 = 0 are concurrent, find the value of k.

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Show that if any line through the variable point A(k+1,2k) meets the l...

    Text Solution

    |

  2. The incident ray is along the line 3x-4y-3=0 and the reflected ray is ...

    Text Solution

    |

  3. If the line y =sqrt(3)x cuts the curve x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. The area of a parallelogram formed by the lines a x+-b y+-c=0 is (a)(c...

    Text Solution

    |

  6. The vertices Ba n dC of a triangle A B C lie on the lines 3y=4xa n dy=...

    Text Solution

    |

  7. If each of the points (x1,4),(-2,y1) lies on the line joining the poi...

    Text Solution

    |

  8. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

    Text Solution

    |

  9. The diagonals of a parallelogram PQRS are along the lines x+3y =4 and ...

    Text Solution

    |

  10. For the straight lines 4x+3y-6=0 and 5x+12 y+9=0, find the equation of...

    Text Solution

    |

  11. A straight line segment of length/moves with its ends on two mutually ...

    Text Solution

    |

  12. Find the foot of the perpendicular from the point (2,4) upon x+y=1.

    Text Solution

    |

  13. The lines x+y-1=0,(m-1)x+(m^2-7)y-5=0, and (m-2)x+(2m-5)y=0 are ...

    Text Solution

    |

  14. In triangleABC, vertex A is (1, 2). If the internal angle bisector of ...

    Text Solution

    |

  15. The equation of the line which bisects the obtuse angle between the li...

    Text Solution

    |

  16. If the line ax+ by =1 passes through the point of intersection of y...

    Text Solution

    |

  17. A straight line L is perpendicular to the line 5x-y=1 . The area of th...

    Text Solution

    |

  18. The reflection of the point (4,-13) about the line 5x+y+6=0 is (-1,-14...

    Text Solution

    |

  19. Triangle A B C with A B=13 ,B C=5, and A C=12 slides on the coordinate...

    Text Solution

    |

  20. The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respec...

    Text Solution

    |