Home
Class 11
MATHS
Show that the lines represented by x(a+3...

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`.

Text Solution

AI Generated Solution

To show that the lines represented by the equation \( x(a + 3b) + y(2a - b) = 5a + b \) pass through a fixed point for different values of \( a \) and \( b \), we can follow these steps: ### Step 1: Rewrite the equation Start with the given equation: \[ x(a + 3b) + y(2a - b) = 5a + b \] Rearranging gives: ...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos
  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|7 Videos
  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|10 Videos

Similar Questions

Explore conceptually related problems

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.

The line, represented by the equation 3x - 8y = 2 , passes through the point (k, 2). Find the value of k.

If a ,b ,c are variables such that 3a+2b+4c=0 , then show that the family of lines givenby a x+b y+c=0 pass through a fixed point. Also, find that 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.

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.

If a and b are two arbitrary constants, then prove that the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through a fixed point. Find that point.

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0 (a) always passes through a fixed point (b) represents the family of parallel lines (c) is always perpendicular to x-axis (d) always has negative slope

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.

Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will represent a family of straight lines passikng through a fixed point iff there exists a linear relation between a , b ,\ a n d\ c dot

If a ,\ b , c are in A.P., then the line a x+b y+c=0 passes through a fixed point. write the coordinates of that point.

NAGEEN PRAKASHAN ENGLISH-STRAIGHT LINES-Exercise
  1. Show that the lines represented by x(a+3b)+y(2a-b)=5a+b pass through a...

    Text Solution

    |

  2. Find the new co-ordinates of the following points when origin is shift...

    Text Solution

    |

  3. At which point the origin should be shifted such that the new co-ordin...

    Text Solution

    |

  4. If the origin is shifted to the point (1,2) then what will be the tran...

    Text Solution

    |

  5. Find the point at which origin is shifted such that the transformed e...

    Text Solution

    |

  6. Find the point at which is shifted such that the transformed equations...

    Text Solution

    |

  7. Shift the origin to a suitable point so that the equation y^2+4y+8x-2=...

    Text Solution

    |

  8. Show that the area of triangle whose vertices are (1,0), (2,4) and (3,...

    Text Solution

    |

  9. Find the slope of the lines whose iclination is given : (i) 45^(@) (...

    Text Solution

    |

  10. Find the inclination of the lines whose slopes are as follows : (i) ...

    Text Solution

    |

  11. Find the slopes of the lines passing through the following points : ...

    Text Solution

    |

  12. If the slope of a line passing through the points (1,4) and (x,2) is 2...

    Text Solution

    |

  13. If the angle of inclination of line joining the points (x,3) and (-2,5...

    Text Solution

    |

  14. If the slop of line joining the points (6,-3) and (x,7) is 2, find the...

    Text Solution

    |

  15. Show that the line joining the points (4,-1) and (-3,3) is parallel to...

    Text Solution

    |

  16. If the line joining the points (5,y) and (4,9) is parallel to the line...

    Text Solution

    |

  17. Show that the line joining the points (4,-3) and (0,7) is perpendicula...

    Text Solution

    |

  18. If the line joining the points (6,-2) and (8,4) is perpendicular to th...

    Text Solution

    |

  19. Without using Pythagoras theorem, show that A(4,4),\ B(3,5)a n d\ C(-1...

    Text Solution

    |

  20. Using slopes, show that the points A(0,5), B(3,2) and C(-1,6) are coll...

    Text Solution

    |

  21. Using the slope of line, show that the points (-1,-2), (0,4), (3,3) an...

    Text Solution

    |