Home
Class 11
MATHS
Find the equations of lines parallel to ...

Find the equations of lines parallel to `3x-4y-5=0` at a unit distance from it.

Text Solution

Verified by Experts

The equation of any line parallel to 3x-4y-5 = 0 is
`3x-4y+lambda =0 " " (1)`
Distance of (1) from 3x-4y-5=0 is 1 unit. Therefore,
`(|5+lambda|)/(5) = 1`
`i.e., lambda =-10 or 0`
Therefore, the required line is 3x-4y-10=0 or 3x-4y=0.
These are the equations of the required lines.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

An equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit distance from the origin is

The equation n s of the lines parallel to 5x-12 y+26=0 and at a distance of 4 units from it are: 5x-12 y-26=0 5x-12 y+26=0 5x-12 y-78=0 (d) 5x-12 y+78=0

Find the equation of the line which is parallel to 3x-2y+5=0 and passes through the point (5,-6) .

Find the equation of the line which is parallel to 3x-2y+5=0 and passes through the point (5,-6)

Find the equation of the straight line parallel to Y - axis and at a distance (i) 3 units to the right (ii) 2 units to the left

Find the equation of line parallel to the y-axis and drawn through the point of intersection of x \ - 7y+\ 5\ =\ 0 and 3x+y =\ 0 .

Find the equation of line parallel to the y-axis and drawn through the point of intersection of x \ 7y+\ 5\ =\ 0 and 3x+y \ 7\ =\ 0 .

Find the equation of the line parallel to yaxis and drawn through the point of intersection of the lines x-7y+5=0 and 3x+y=0 .

Find the equation of a line perpendicular to the line 3x+y+5=0 and at a distance of 3 units from the origin.

Find the general equation of the line which is parallel to 3x-4y+5 = 0 . Also find such line through the point (-1,2)

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. The ratio in which the line 3x+4y+2=0 divides the distance between 3x+...

    Text Solution

    |

  2. Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Fin...

    Text Solution

    |

  3. Find the equations of lines parallel to 3x-4y-5=0 at a unit distance f...

    Text Solution

    |

  4. Let P (sin theta, cos theta) (0 le theta le 2pi) be a point and let OA...

    Text Solution

    |

  5. Find the equation of a straight line passing through the point (-5,4) ...

    Text Solution

    |

  6. If A(x1, y1),B(x2, y2),C(x3, y3) are the vertices of a triangle, then...

    Text Solution

    |

  7. Are the points (3,4) and (2,-6) on the same or opposite sides of the l...

    Text Solution

    |

  8. Consider the equation y-y1=m(x-x1) . If m and x1 are fixed and differe...

    Text Solution

    |

  9. एक रेखा ऐसी है कि लाइनों 5 x − y + 4 = 0 तथा 3 x + 4 y − 4 = 0के बीच...

    Text Solution

    |

  10. If the straight line a x+c y=2b , where a , b , c >0, makes a tri...

    Text Solution

    |

  11. A B C D is a square whose vertices are A(0,0),B(2,0),C(2,2), and D(0,2...

    Text Solution

    |

  12. The x-coordinates of the vertices of a square of unit area are the r...

    Text Solution

    |

  13. Consider a triangle with vertices A(1,2),B(3,1) and C(-3,0). Find the...

    Text Solution

    |

  14. If (x , y) is a variable point on the line y=2x lying between the li...

    Text Solution

    |

  15. A rectangle has two opposite vertices at the points (1, 2) and (5,5). ...

    Text Solution

    |

  16. If D , E ,a n dF are three points on the sides B C ,A C ,a n dA B of a...

    Text Solution

    |

  17. Find the coordinates of the foot of the perpendicular drawn from the ...

    Text Solution

    |

  18. Let the sides of a parallelogram be U=a, U=b,V=a' and V=b', where U=l...

    Text Solution

    |

  19. Find the image of the point (-8,12) with respect to line mirror 4x+7y+...

    Text Solution

    |

  20. One side of a rectangle lies along the line 4x+7y+5=0. Two of its vert...

    Text Solution

    |