Home
Class 11
MATHS
A variable straight line drawn through t...

A variable straight line drawn through the point of intersection of the straight lines `x/a+y/b=1` and `x/b+y/a=1` meets the coordinates axes at A and B. Show that the locus of the mid point of `bar(AB)` is `2(a+b)xy=ab(x+y)`.

Text Solution

Verified by Experts

The correct Answer is:
`ab(x+y)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-3(a)) |37 Videos

  • STRAIGHT LINE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-3(b)) |29 Videos

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(b) ) III.|11 Videos

  • TELANGANA MARCH 2015

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Section - C (Long answer type questions)|6 Videos

Similar Questions

Explore conceptually related problems

Find the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1, (a!=+-b)

A variable line drawn throgh the point of intersection of the lines x/a+y/b=1,x/b+y/a=1 meets the coordinate axes in A and B. Then the locus of midpoint of AB is

The equation of the straight line passing through the point of intersection of the straight lines x/a+x/b=1 and x/b+y/a=1 and having infinite slope is

The vertical straight line passing through the point of intersection of the straight lines x-3y+1=0, 2x+5y-9=0 and at a distance of 2 units from the origin has the equation

If a circle passes through the points of intersection of the axes with the lines ax-y+1=0 and x-2y+3=0 then a=

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the middle point of the segment AB has the eqution

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the feet of the perpendicular from the origin on the variable line L has the equation

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-STRAIGHT LINE -TEXTUAL EXERCISES (EXERCISE-3(e))
  1. A variable straight line drawn through the point of intersection of th...

    Text Solution

    |

  2. Find the incentre of the Delta^(l e) with the vertices (1,sqrt3),(0,0)...

    Text Solution

    |

  3. Find the orthocentre of the triangle whose sides are given by x+y+10=0...

    Text Solution

    |

  4. The orthocentre of the triangle whose sides are given by 4x-7y+10=0,x+...

    Text Solution

    |

  5. Find the circumcentre of the triangle whose sides are 3x-y-5=0, x+2y-4...

    Text Solution

    |

  6. The incentre of the triangle formed by the lines x+y=1,x=1,y=1 is

    Text Solution

    |

  7. Find the circumcentre of the triangle whose vertices are A(1,0),B(-1,2...

    Text Solution

    |

  8. Find the value of k if the angle between the straight kx+y+9=0, 3x-y+4...

    Text Solution

    |

  9. Find the equation of the straight line passing through (0,0) and also ...

    Text Solution

    |

  10. Find the equation of the straight line parallel to 3x+4y=7 and passing...

    Text Solution

    |

  11. The equation of the straight line perpendicular to the straight line 3...

    Text Solution

    |

  12. Find the equation of the straight line making non zero equal intercept...

    Text Solution

    |

  13. Find the point of intersection of the lines 4x+8y-1=0, 2x-8y+1=0

    Text Solution

    |

  14. Find the value of a if the distances of the points (2,3) and (-4,a) fr...

    Text Solution

    |

  15. Find the circumcentre of the triangle formed by the lines x+y=0, 2x+y+...

    Text Solution

    |

  16. If theta is the angle between the lines x/a+y/b=1 and x/b+y/a=1 find t...

    Text Solution

    |

  17. Find the equation of the straight lines passing through the point (-10...

    Text Solution

    |

  18. Find the equation of the straight lines passing through the point (1,2...

    Text Solution

    |

  19. The base of an equilateral triangle x + y = 2 = 0 and opposite vertex...

    Text Solution

    |

  20. Find the orthocentre of the triagle whose vertices are (-2,-1)(6,-1),(...

    Text Solution

    |

  21. Find the orthocentre of the triangle whose vertices are (5,-2),(-1,2),...

    Text Solution

    |