Home
Class 11
MATHS
The lines L1:y-x =0 and L2: 2x+y =0 inte...

The lines `L_1`:y-x =0 and `L_2`: 2x+y =0 intersect the line `L_3` : y+2 =0 at P and Q respectively. The bisector of the acute angle between `L_1` and `L_2` intersects `L_3` at R
Statement - 1 : The ratio PR : PQ equals `2sqrt2 : sqrt5`
Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar 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 equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is

Find the bisector of the angle containing the point (1,-2) between the lines 3x-4y = 0 and 5x + 12y +7 = 0

The line L given by x/5 + y/b = 1 passes through the point (13,32).the line K is parallel to L and has the equation x/c+y/3=1 then the distance between L and K is

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is

A straight lines L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Q two straight lines L_1 and L_2 are drawn, parallel to 2x-y=5 and 3x+y=5 respectively. Line L_1 and L_2 intersect at R. Show that the locus of R as L varies is a straight line.

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Lines L_1-=a x+b y+c=0 and L_2-=l x+m y+n=0 intersect at the point P and make an angle theta with each other. Find the equation of a line different from L_2 which passes through P and makes the same angle theta with L_1dot

The equations of bisectors of two lines L_1 & L_2 are 2x-16y-5=0 and 64x+ 8y+35=0 . lf the line L_1 passes through (-11, 4) , the equation of acute angle bisector of L_1 & L_2 is:

Consider the lines L_(1) -=3x-4y+2=0 " and " L_(2)-=3y-4x-5=0. Now, choose the correct statement(s).

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. The straight lines 4a x+3b y+c=0 passes through which point? , where a...

    Text Solution

    |

  2. The line parallel to the x-axis and passing through the intersection o...

    Text Solution

    |

  3. The lines L1:y-x =0 and L2: 2x+y =0 intersect the line L3 : y+2 =0 at ...

    Text Solution

    |

  4. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

    Text Solution

    |

  5. Two sides of a rhombus ABCD are parallel to the lines y=x+2 and y=7x+3...

    Text Solution

    |

  6. Equation(s) of the straight line(s), inclined at 30^(@) to the x-axis ...

    Text Solution

    |

  7. If a pair of perpendicular straight lines drawn through the origin f...

    Text Solution

    |

  8. The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0....

    Text Solution

    |

  9. The image of P(a,b) on the line y=-x is Q and the image of Q on the li...

    Text Solution

    |

  10. Consider a DeltaABC whose sides AB, BC and CA are represented by the s...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |