Home
Class 11
MATHS
Find the point of intersection of the fo...

Find the point of intersection of the following pairs of lines: `y=m_1x+a/(m_1)\ a n d\ y=m_2x+a/(m_2)dot`

Text Solution

Verified by Experts

`y=m_1x+a/(m_1) .....(1)`
`y=m_2x+a/(m_2)dot`........(2)
Solving (1) and (2) using cross - multiplication method
`x/((-a/m_2)+(a/m_1))=y/((am_2/m_1)-(am_1/m_2))=1/(-m_1+m_2)`
`x=a/(m_1m_2) and y=a(m_1+m_2)/(m_1m_2)`
Promotional Banner

Topper's Solved these Questions

  • THE CIRCLE

    RD SHARMA|Exercise Solved Examples And Exercises|144 Videos

  • TRANSFORMATION FORMULAE

    RD SHARMA|Exercise Solved Examples And Exercises|145 Videos

Similar Questions

Explore conceptually related problems

Find the point of intersection of the following pair of lines : (i) 9x-10y=12 and 2x-5=0 (ii) y=m_(1)x+c_(1) and y=m_(2)x+c_(2) (iii) x+y=8 and x-y=2

Determine the distance between the following pair of parallel lines: y=m x+c\ a n d\ y=m x+d

Find the equations of the straight lines , bisectors of the angles formed by the following pairs of lines y-b=(2m)/(1-m^(2))(x-a) and y-b=(2m')/(1-m' ^(2))(x-a)

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is 2 (b) 0 (c) 4 (d) 1

What is the locus fo t he point of intersection of the striaght lines (x//a)+(y//b) =m and (x//a)-(y//b)=1//m ?

Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

The locus of point of intersection of the lines y+mx=sqrt(4+m^(2)) and my-x=sqrt(1+4m^(2)) is x^(2)+y^(2)=k then "k" is

If m is a variable,then prove that the locus of the point of intersection of the lines (x)/(3)-(y)/(2)=m and (x)/(3)+(y)/(2)=(1)/(m) is a hyperbola.

RD SHARMA-THE STRAIGHT LINES -Solved Examples And Exercises
  1. Find the point of intersection of the following pairs of lines: 2x-y+3...

    Text Solution

    |

  2. Find the point of intersection of the following pairs of lines: b x+a ...

    Text Solution

    |

  3. Find the point of intersection of the following pairs of lines: y=m1x+...

    Text Solution

    |

  4. Find the coordinates o the vertices of a triangle, the equations of ...

    Text Solution

    |

  5. Find the coordinates o the vertices of a triangle, the equations of ...

    Text Solution

    |

  6. Show that the area of the triangle formed by the lines y=m1x+c1,""...

    Text Solution

    |

  7. Find the area of triangle formed by the lines : y=0,\ x=2\ a n d\ x+2y...

    Text Solution

    |

  8. Find the area of triangle formed by the lines :\ x+y-6=0,\ x-3y-2=0\ a...

    Text Solution

    |

  9. Find the equations of the medians of a triangle, the equations of whos...

    Text Solution

    |

  10. Prove that the lines y=sqrt3x+1,\ y=4\ n d\ y=-sqrt3x+2 form an equila...

    Text Solution

    |

  11. Classify the following pairs of lines as coincident, parallel or in...

    Text Solution

    |

  12. Classify the following pairs of lines as coincident, parallel or in...

    Text Solution

    |

  13. Find the equation of the line joining the point (3,5) to the point of ...

    Text Solution

    |

  14. Find the equation of the lien passing through the point of intersectio...

    Text Solution

    |

  15. Show that the area of the triangle formed buy the lines y=m1x , y=m2x\...

    Text Solution

    |

  16. Prove that the lines sqrt(3)x+y=0,\ sqrt(3)y+x=0,\ sqrt(3)x+y=1\ a n d...

    Text Solution

    |

  17. Find the equation of the line passing through the intersection of the ...

    Text Solution

    |

  18. Prove that the lies 3x+y-14=0,\ x-2y=0\ n a d\ 3x-8y+4=0 are concurren...

    Text Solution

    |

  19. If the lines a1x+b1y+1=0,\ a2x+b2y+1=0\ a n d\ a3x+b3y+1=0 are concurr...

    Text Solution

    |

  20. Show that the following lines are concurrent: L1=(a-b)x+(b-c)y+(c-a)=0...

    Text Solution

    |