Home
Class 12
MATHS
A variable straight line passes through ...

A variable straight line passes through the points of intersection of the lines `x +2y= 1` and `2x-y = 1` and meets the co-ordinates axes in `A` and `B`. Prove that the locus of the midpoint Of `AB` is `10xy = x + 3y`.

A

`x-3y=10xy`

B

`x+3y=10xy`

C

`3x+y=10xy`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    MTG-WBJEE|Exercise WB JEE Previous Years Questions|28 Videos

  • STATISTICS AND PROBABILITY

    MTG-WBJEE|Exercise WB JEE Previous Years Questions ( CATEGORY 3 : One or More than One Option Correct Type ( 2 Marks) )|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 1 : Single Option Correct Type)|10 Videos

Similar Questions

Explore conceptually related problems

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

If a variable line passes through the point of intersectionof the lines x+2y-1=0 and 2x-y-1=0 and meets the coordinate axes in A and B ,then the locus of the midpoint of AB is : (A)x+3y=0 (B) x+3y=10(C)x+3y=10xy(D) None of these

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

A variable line through the point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 meets the coordinate axes in A and B.Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

A variable line through the point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 meets the coordinate axes in A and B.Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

A variable line through the point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 meets the coordinate axes in A and B.Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

A variable line through the point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 meets the coordinate axes in A and B.Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

MTG-WBJEE-STRAIGHT LINES-WB JEE Previous Years Questions
  1. A variable straight line passes through the points of intersection of ...

    Text Solution

    |

  2. If a , ba n dc are in A P , then the straight line a x+b y+c=0 will al...

    Text Solution

    |

  3. The equation 2x^(2) + 5xy-12y^(2)=0 respresents a

    Text Solution

    |

  4. The number of lines which pass through the point (2,-3) and are at a d...

    Text Solution

    |

  5. The straight lines x +y=0, 5x + y= 4 and x+5y=4 form (A) an isosceles ...

    Text Solution

    |

  6. If the point (2 cos theta, 2 sin theta), for theta in (0, 2pi) lines i...

    Text Solution

    |

  7. Number of points having distance sqrt5 from the straight line x-2y+1=0...

    Text Solution

    |

  8. The points (-a,-b), (0,0). (a,b) and (a^(2),a^(3)) are

    Text Solution

    |

  9. The line AB cuts off equal intercepts 2a from the axes. From any point...

    Text Solution

    |

  10. The line through the points (a, b) and (-a, - b) passes through the po...

    Text Solution

    |

  11. Let S be the set of points whose abscissas and ordinates are natural n...

    Text Solution

    |

  12. x + 8y -22=0, 5x +2y-34 =0, 2x - 3y +13 = 0 are the three sides of a t...

    Text Solution

    |

  13. Transforming to parallel axes through a point (p, q), the equation 2(x...

    Text Solution

    |

  14. Let A (2,-3) and B (-2,1) be the vertices of Delta ABC. If the centro...

    Text Solution

    |

  15. The point P(3, 6) is first reflected on the line y = X and then the im...

    Text Solution

    |

  16. Let d1 and d2 be the lengths of the perpendiculars drawn from any po...

    Text Solution

    |

  17. The point Q is the image of the point P(1,5) about the line y=x and R ...

    Text Solution

    |

  18. The vertices of a triangle are A (-1, -7), B (5, 1) and C(1, 4). The ...

    Text Solution

    |

  19. The variable line drawn through the point (1, 3) meets the x-axis at A...

    Text Solution

    |

  20. A straight line L through the point (3,-2) is inclined at an angle 60^...

    Text Solution

    |

  21. A variable line passes through the fixed point (alpha, beta). The locu...

    Text Solution

    |