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

A

statement - 1 is true, Statement - 2 is true :
Statement -2 is not correct explanation for statement -1

B

Statement -1 is true , Statement -2 is false

C

Statement -1 is false, statement -2 is true

D

Statement -1 is true statement -2 is true , Statement-2 is a correct explanation for Statement -1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos
  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 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).

PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. The least positive value of t so that the lines x = t+alpha, y+16 = 0 ...

    Text Solution

    |

  2. If the point (2costheta, 2sintheta), for theta in (0 ,2pi) lies in th...

    Text Solution

    |

  3. Number of points having distance sqrt5 from the straight line x-2y+1 =...

    Text Solution

    |

  4. For agtbgtcgt0, the distance between (1 ,1) and the point of intersect...

    Text Solution

    |

  5. A ray light along x+sqrt3y = sqrt3 gets reflected upon reaching the x-...

    Text Solution

    |

  6. The x co -ordinate of the incentre of the triangle that has the coordi...

    Text Solution

    |

  7. The equation 2x^2+5xy - 12y^2=0 represents a

    Text Solution

    |

  8. The number of lines which pass through the point (2 , -3) and are the ...

    Text Solution

    |

  9. If the line 2x + y = k passes through the point which divides the line...

    Text Solution

    |

  10. A line is drawn through the point ( 1, 2) to meet the coordinate axes ...

    Text Solution

    |

  11. Let P(2 ,3), Q ( -2 ,1) be the vertices of the triangle PQR .If the ce...

    Text Solution

    |

  12. The number of integral values of 'm' for which the x coordinate of the...

    Text Solution

    |

  13. If a straight line passes through the point (alpha ,beta) and the port...

    Text Solution

    |

  14. The line joining A (b cos alpha, b sin alpha ) and B (a cos beta, a si...

    Text Solution

    |

  15. A straight line through the point of intersection of the lines x+2y =...

    Text Solution

    |

  16. A straight lines L through the point ( 3, 2) is inclined at an angle ...

    Text Solution

    |

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

    Text Solution

    |

  18. The coordinates of the two points lying on x + y = 4 and at a unit dis...

    Text Solution

    |

  19. If the three points A (1, 6), B(3,-4) and C(x,y) are collinear then th...

    Text Solution

    |

  20. Find the image of the point (-8,12) which respect to the line 4x + 7y...

    Text Solution

    |