Home
Class 11
MATHS
The sides of a triangle have the combine...

The sides of a triangle have the combined equation `x^2-3y^2-2x y+8y-4=0` . The third side, which is variable, always passes through the point `(-5,-1)` . Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

The equations of two sides of a triangle are 3y-x-2=0a n dy+x-2=0. The third side, which is variable, always passes through the point (5,-1) . Find the range of the values of the slope of the third side, so that the origin is an interior point of the triangle.

Two sides of a square have the equations 5x + 12 y = 10 and 5x + 12y + 29 = 0 and the third side passes through the point (3,5) . Find the equations of the other two sides of the square.

Two sides of an isoceles triangle are given by the equations 7x-y+3=0andx+y-3=0 and its third side passes through the point (1,-10) . Determine the equation of the third side.

Find the equation of the line which is parallel to 3x-2y+5=0 and passes through the point (5,-6) .

The slope of a curve at (x,y) is (x^(2)-2) and it passes through the point (3,8) . Find the equation of the curve

Find the equation of a circle which is passes through the point (4,3) and (-2,.5) and the centre lies on the straight line 2x - 3y = 4.

Two equal sides of an isosceles triangle are given by 7x-y+3=0 and x+y=3 , and its third side passes through the point (1,-10) . Find the equation of the third side.

Two sides of a triangle are the lines (a+b)x+(a-b)y-2ab=0 and (a-b)x+(a+b)y-2ab=0 . If the triangle is isosceles and the third side passes through point (b-a,a-b) then the equation of third side can be :

The equations of the two sides of a square are 5x+12y-26=0 and 5x+12y+13=0. If one of the remaining sides passes through the point (5,-1) ,find the equations of of these sides.

Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of the triangle is the origin, find the coordinates of the third point.

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. Consider a DeltaABC whose sides AB, BC and CA are represented by the s...

    Text Solution

    |

  2. Area of the triangle formed by the line x+y=3 and the angle bisectors ...

    Text Solution

    |

  3. The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=...

    Text Solution

    |

  4. The equation of the lines passing through the point (1,0) and at a dis...

    Text Solution

    |

  5. The number of values of k for which the lines (k+1)x+8y=4k and kx+(k+3...

    Text Solution

    |

  6. For all real values of a and b lines (2a+b)x + (a+3b)y+(b-3a)=0 and mx...

    Text Solution

    |

  7. The line x=c cuts the triangle with corners (0,0),(1,1) and (9,1) into...

    Text Solution

    |

  8. The absolute value of the sum of the abscissas of all the points on th...

    Text Solution

    |

  9. The point (x , y) lies on the line 2x+3y=6. The smallest value of the ...

    Text Solution

    |

  10. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

    Text Solution

    |

  11. One of the diagonals of a square is the portion of the line x/2+y/3=2 ...

    Text Solution

    |

  12. Two sides of a triangle are along the coordinate axes and the medians ...

    Text Solution

    |

  13. The graph of y^2+2x y+40|x|=400 divides the plane into regions. Then ...

    Text Solution

    |

  14. In a triangle A B C ,A=(alpha,beta)B=(2,3),a n dC=(1,3)dot Point A lie...

    Text Solution

    |

  15. If the straight lines 2x+3y-1=0,x+2y-1=0,and ax+by-1=0form a triangle ...

    Text Solution

    |

  16. Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such...

    Text Solution

    |

  17. If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 s...

    Text Solution

    |

  18. In a triangle A B C , the bisectors of angles Ba n dC lies along the l...

    Text Solution

    |

  19. If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the fam...

    Text Solution

    |

  20. P(m , n) (where m , n are natural numbers) is any point in the interio...

    Text Solution

    |