• NEET
      • Class 11th
      • Class 12th
      • Class 12th Plus
    • JEE
      • Class 11th
      • Class 12th
      • Class 12th Plus
    • Class 6-10
      • Class 6th
      • Class 7th
      • Class 8th
      • Class 9th
      • Class 10th
    • View All Options
      • Online Courses
      • Distance Learning
      • Hindi Medium Courses
      • International Olympiad
    • NEET
      • Class 11th
      • Class 12th
      • Class 12th Plus
    • JEE (Main+Advanced)
      • Class 11th
      • Class 12th
      • Class 12th Plus
    • JEE Main
      • Class 11th
      • Class 12th
      • Class 12th Plus
  • Classroom
    • NEET
      • 2025
      • 2024
      • 2023
      • 2022
    • JEE
      • 2025
      • 2024
      • 2023
      • 2022
    • Class 6-10
    • JEE Main
      • Previous Year Papers
      • Sample Papers
      • Result
      • Analysis
      • Syllabus
      • Exam Date
    • JEE Advanced
      • Previous Year Papers
      • Sample Papers
      • Mock Test
      • Result
      • Analysis
      • Syllabus
      • Exam Date
    • NEET
      • Previous Year Papers
      • Sample Papers
      • Mock Test
      • Result
      • Analysis
      • Syllabus
      • Exam Date
      • College Predictor
      • Counselling
    • NCERT Solutions
      • Class 6
      • Class 7
      • Class 8
      • Class 9
      • Class 10
      • Class 11
      • Class 12
    • CBSE
      • Notes
      • Sample Papers
      • Question Papers
    • Olympiad
      • NSO
      • IMO
      • NMTC
  • NEW
    • TALLENTEX
    • AOSAT
  • ALLEN E-Store
    • ALLEN for Schools
    • About ALLEN
    • Blogs
    • News
    • Careers
    • Request a call back
    • Book home demo
Home
Class 11
MATHS
Show that the straight lines given by (2...

Show that the straight lines given by `(2+k)x+(1+k)y=5+7k` for different values of `k` pass through a fixed point. Also, find that point.

To view this video, please enable JavaScript and consider upgrading to a web browser thatsupports HTML5 video

Text Solution

AI Generated Solution

To show that the straight lines given by the equation \((2+k)x + (1+k)y = 5 + 7k\) pass through a fixed point for different values of \(k\), we will rearrange the equation and find the point where these lines intersect. ### Step-by-step Solution: 1. **Start with the given equation:** \[ (2+k)x + (1+k)y = 5 + 7k \] ...
Doubtnut Promotions Banner Desktop LightDoubtnut Promotions Banner Desktop DarkDoubtnut Promotions Banner Mobile LightDoubtnut Promotions Banner Mobile Dark

Topper's Solved these Questions

  • THE CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos
  • TRANSFORMATION FORMULAE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos

Similar Questions

Explore conceptually related problems

Show that the straight lines given by x(a+2b)+y(a+3b)=a for different values of a and b pass through a fixed point.

Show that the straight lines given by x(a+2b)+y(a+3b)=a for different values of a and b pass through a fixed point.

Prove that the line x(a+2b) + y (a-3b)=a-b passes through a fixed point for different values of a and b . Also find the fixed point.

(1) The straight lines (2k+3) x + (2-k) y+3=0 , where k is a variable, pass through the fixed point (-3/7, -6/7) . (2) The family of lines a_1 x+ b_1 y+ c_1 + k (a_2 x + b_2 y + c_2) = 0 , where k is a variable, passes through the point of intersection of lines a_1 x + b_1 y + c_1 = 0 and a_2 x+ b_2 y + c_2 = 0 (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Show that the lines represented by x(a+3b)+y(2a-b)=5a+b pass through a fixed point for different values of a and b .

A circle passes through a fixed point A and cuts two perpendicular straight lines through A in B and C. If the straight line BC passes through a fixed-point (x_(1), y_(1)) , the locus of the centre of the circle, is

Show that the locus of the middle point of all chords of the parabola y^2 = 4ax passing through a fixed point (h, k) is y^2 - ky=2a(x-h) .

Find the point of intersection of the lines 4x + 3y = 1 and 3x - y + 9 = 0 . If this point lies on the line (2k - 1) x - 2y = 4 , find the value of k. The above question can also be stated as : If the lines 4x + 3y = 1, 3x – y + 9 = 0 and (2k - 1) x - 2y = 4 are concurrent (pass through the same point), find the value of k.

The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0, find the value of k. Also, find the co-ordinates of point Q.

Find the value of k if the points (2,3) , (5,k) and (6,7) are collinear .

RD SHARMA ENGLISH-THE STRAIGHT LINES -All Questions
  1. Show that the straight lines given by (2+k)x+(1+k)y=5+7k for different...

    04:33

    |

  2. Find the equation of the internal bisector of angle B A C of the trian...

    09:28

    |

  3. The ratio in which the line segment joining (-1,1) and (5,7) is divide...

    03:55

    |

  4. The mid points of the sides of a triangle are (2,1), (-5,7) and (-5,-5...

    07:34

    |

  5. Find the equation of the altitudes of the triangle whose vertices are ...

    06:26

    |

  6. One side of a square makes an angle alpha with x axis and one vertex o...

    10:03

    |

  7. Show that the perpendicular drawn from the point (4,1) on the line seg...

    09:12

    |

  8. Prove that the perpendicular drawn from the point (4,1) on the join of...

    08:40

    |

  9. A line passing through the point A(3,0) makes 30^0 angle with the posi...

    05:36

    |

  10. In what ratio is the line joining the points (2,3)a n d(4,1) divides t...

    07:06

    |

  11. Find the equations to the altitudes of the triangle whose angular p...

    08:54

    |

  12. Find the equations of the diagonals of the square formed by the lines ...

    04:40

    |

  13. Find the equation of a line which cuts off intercepts a and b respec...

    03:00

    |

  14. Find the equation of the bisector of angle A ofthe triangle whoe verti...

    07:02

    |

  15. Find the equations of the straight lines which go through the origin a...

    17:38

    |

  16. A line L is such that its segment between the straight lines 5x - y ...

    05:37

    |

  17. Find the equations to the diagonals of the rectangle the equations of ...

    05:20

    |

  18. A rectangle has two opposite vertices at the points (1,2) a n d (5,5)....

    06:56

    |

  19. Find the coordinates of the vertices of a square inscribed in the tria...

    06:29

    |

  20. If the intercept of a line between the coordinate axes is divided by ...

    04:48

    |

Home
Profile
|