Home
Class 12
MATHS
The equation of set of lines which are a...

The equation of set of lines which are at a constant distance 2 units from the origin is

A

x+y+2=0

B

x+y+4=0

C

`x "cos" alpha + y "sin" alpha = 2`

D

`x "cos" alpha + y "sin" alpha = (1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
If normal to the line make an angle `alpha` with x-axis, then equation of line is
`x"cos"alpha+y"sin"alpha = p,` where p is distance of line from origin.
Here, p=2
So, equation of lines is `x"cos"alpha+y"sin"alpha = 2.`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (LINKED COMPREHENSION TYPE)|27 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Find the equations to the straight lines which are at a distance of 2 unit from the origin and which pass throught the points (4,-2).

Find the equations to the straight lines which are at a distance of 2 unit from the origin and which pass through the point of intersection of the lines 3x+4y=4 and 2x+5y+2=0 .

Form the differential equation of family of lines situated at a constant distance p from the origin.

Find the equations to the straight lines which are at a distance of 1 unit from the origin and which pass through the point (3,1).

Find the equations to the straight lines which are at a distance of 3 unit from the origin and which pass through the intersection of the lines 4x+3y+1=0 and 5x-y=13

Find the equation of the circle which touches the x-axis at a distance +5 unit from the origin and cuts off an intercept of length 24 unit from the y-axis.

The equations of the circel which touch the x axis at a distance of 3 unit from the origin and intercepts a chord of length 6 unit on the y-axis, aer-

Find the vector equation of a plane which is at a distance of (6)/(sqrt29) units from the origin and which is normal to 2 hati-3 hatj+ 4 hatk . Convert it into cartesian from.

Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30^0 with the positive direction of the x-axis.

Find the vector equation of a plane which is at distance of 3 units from the origin and has 2,2,-1 as the direction ratios of a normal to it.Also find the position vector of the foot of the prependicular drown from the origin to it .

CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
  1. The number of integral values of m for which the x-coordinate of the p...

    Text Solution

    |

  2. If the sum of the distances of a point from two perpendicular lines in...

    Text Solution

    |

  3. The equation of set of lines which are at a constant distance 2 units...

    Text Solution

    |

  4. The lines y=m1x ,y=m2xa n dy=m3x make equal intercepts on the line x+y...

    Text Solution

    |

  5. Find the condition in a,b such that the portion of the line ax+by=1, i...

    Text Solution

    |

  6. The area of the triangle formed by the lines y= ax, x+y-a=0, and y-axi...

    Text Solution

    |

  7. The line x/a+y/b=1 meets the x-axis at A , the y-axis at B , and the l...

    Text Solution

    |

  8. The line x/3+y/4=1 meets the y-axis and x-axis at A and B respectively...

    Text Solution

    |

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

    Text Solution

    |

  10. One diagonal of a square is 3x-4y+8=0 and one vertex is (-1,1), then t...

    Text Solution

    |

  11. In an isoceles triangle OAB , O is the origin and OA=OB=6 . The equati...

    Text Solution

    |

  12. Find the sum of the series 1^2-2^2+3^2-4^2+\ldots-{2008}^2+{2009}^2

    Text Solution

    |

  13. The coordinates of the foot of the perpendicular from the point (2,3) ...

    Text Solution

    |

  14. The straight lines 7x-2y+10=0 and 7x+2y-10=0form an isosceles triangle...

    Text Solution

    |

  15. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

    Text Solution

    |

  16. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

    Text Solution

    |

  17. The range of values of theta in the interval (0, pi) such that the poi...

    Text Solution

    |

  18. Distance of origin from the line (1+sqrt3)y+(1-sqrt3)x=10 along the li...

    Text Solution

    |

  19. Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x...

    Text Solution

    |

  20. Consider the point A(3,4) and B(7,13).If P be a point on the line y=x,...

    Text Solution

    |