Home
Class 11
MATHS
A Line through the variable point A(1+k,...

A Line through the variable point `A(1+k,2k)` meets the lines `7x+y-16=0; 5x-y-8=0 and `x-5y+8=0` at B,C,D respectively. Prove that AC;AB and AD are in HP.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

A straight line through the point A (-2,-3) cuts the line x+3y=9 and x+y+1=0 at B and C respectively. If AB.AC =20 then equation of the possible line is

The intercepts of the straight line 7x+8y-56=0 on x and y axes are respectively-

Prove that the lines 2x-3y-7=0,3x-4y-13=0 and 8x-11y-33=0 are concurrent.

A line through A(-5,-4) meets the lines x+3y+2=0, 2x+y+4=0 and x-y-5=0 at the points B, C and D respectively. If (15/(AB))^2+(10/(AC))^2=(6/(AD))^2 find the equation of the line.

The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respectively. Find Coordinates of P on y=(3x)/4 such that PA*PB=25.

The point (8,-9) with respect to the lines 2x+3y-4=0 and 6x+9y+8=0 lies on

Find the bisector of the angle containing the point (1,-2) between the lines 3x-4y = 0 and 5x + 12y +7 = 0

If sum of the perpendicular distances of a variable point P(x, y) from the lines x + y - 5 = 0 " and " 3x - 2y + 6 = 0 is always 10. Show that P must move on a line.

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. Show that the lines 4x+y-9=0, x-2y+3=0, 5x-y-6=0 make equal intercepts...

    Text Solution

    |

  2. Find the equation of the bisector of the obtuse angle between of the l...

    Text Solution

    |

  3. A Line through the variable point A(1+k,2k) meets the lines 7x+y-16=0;...

    Text Solution

    |

  4. The incident ray is along the line 24x+7y+5=0. Find the equation of mi...

    Text Solution

    |

  5. If the line y =sqrt(3)x cuts the curve x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=...

    Text Solution

    |

  6. Two equal sides of an isosceles triangle are 7x-y+3=0 and x+y-3=0. Its...

    Text Solution

    |

  7. The area of a parallelogram formed by the lines a x+-b y+-c=0 is

    Text Solution

    |

  8. The vertices, B and C of a triangle ABC lie on the lines 3y=4x and y=...

    Text Solution

    |

  9. If each of the points (x1, 4), (-2,y1) lies on the line joining the po...

    Text Solution

    |

  10. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

    Text Solution

    |

  11. The diagonals of a parallelogram PQRS are along the lines x+3y =4 and ...

    Text Solution

    |

  12. For the straight lines 4x+3y-6 = 0 and 5x+12y+9 = 0, find the equation...

    Text Solution

    |

  13. A straight line segment AB of length 'a' moves with its ends on the ax...

    Text Solution

    |

  14. Find the foot of the perpendicular from the point (2,4) upon x+y=1.

    Text Solution

    |

  15. The lines x+y-1=0,(m-1)x+(m^2-7)y-5=0, and (m-2)x+(2m-5)y=0 are (a)con...

    Text Solution

    |

  16. In Delta ABC , vertex A is (1,2). If the internal angle bisector of an...

    Text Solution

    |

  17. Find the equation of the bisector of the obtuse angle between of the l...

    Text Solution

    |

  18. The line ax+by=1 passes through the point of intertsection of y=x tan ...

    Text Solution

    |

  19. A straight line L is perpendicular to the line 5x-y=1. The aera of the...

    Text Solution

    |

  20. The reflection of the point (4,-13) about the line 5x+y+6=0 is a. (-1,...

    Text Solution

    |