Home
Class 12
MATHS
Equation(s) of the straight line(s), inc...

Equation(s) of the straight line(s), inclined at `30^0` to the x-axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units, is (are) (a) `x+sqrt(3)y+5sqrt(3)=0` (b)`x-sqrt(3)y+5sqrt(3)=0` (c)`x+sqrt(3)y-5sqrt(3)=0` (d)`x-sqrt(3)y-5sqrt(3)=0`

A

`x+sqrt(3)y+5sqrt(3)=0`

B

`x-sqrt(3)y+5sqrt(3)=0`

C

`x+sqrt(3)y-5sqrt(3)=0`

D

`x-sqrt(3)y-5sqrt(3)=0`

Text Solution

Verified by Experts

The correct Answer is:
B, D

According to the question, AB=10. So, OA=10 `"sin"30^(@) =5`. Then the equation of line is
`y=(1)/(sqrt(3)) x +-5`
`"or " x-sqrt(3)y+-5sqrt(3)=0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Comprehension)|27 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Matrix)|8 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Single)|82 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

Solve sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

The equation of a straight line on which the length of perpendicular from the origin is four units and the line makes an angle of 120^0 with the x-axis is (A) xsqrt(3)+y+8=0 (B) xsqrt(3)-y=8 (C) xsqrt(3)-y=8 (D) x-sqrt(3)y+8=0

Solve : sqrt(3)x^(2)+5x+2sqrt(3)=0

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

Find the equation of the straight line which passes through the origin and makes angle 60^0 with the line x+sqrt(3)y+sqrt(3)=0 .

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)

Solve, using the method of substitution sqrt( 2)x - sqrt(3) y =1, sqrt(3) x - sqrt( 8) y = 0

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

CENGAGE-STRAIGHT LINES-Exercise (Multiple)
  1. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= 1/(2(1+x)sqrt(x)) (b) 3/((1+...

    Text Solution

    |

  2. The equation of the lines passing through the point (1,0) and at a dis...

    Text Solution

    |

  3. The sides of a triangle are the straight lines x+y=1,7y=x , and sqrt(3...

    Text Solution

    |

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

    Text Solution

    |

  5. Consider the equation y-y1=m(x-x1) . If ma n dx1 are fixed and differe...

    Text Solution

    |

  6. Equation(s) of the straight line(s), inclined at 30^0 to the x-axis su...

    Text Solution

    |

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

    Text Solution

    |

  8. The equation of a straight line passing through the point (2, 3) and ...

    Text Solution

    |

  9. The equation of the line on which the perpendicular from the origin ma...

    Text Solution

    |

  10. A line is drawn perpendicular to line y=5x , meeting the coordinate ax...

    Text Solution

    |

  11. If x-2y+4=0a n d2x+y-5=0 are the sides of an isosceles triangle having...

    Text Solution

    |

  12. The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, a...

    Text Solution

    |

  13. Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concur...

    Text Solution

    |

  14. The equation of bisector of two lines L(1) " and " L(2) are 2x-16y-5=0...

    Text Solution

    |

  15. Consider the lines L(1) -=3x-4y+2=0 " and " L(2)-=3y-4x-5=0. Now, choo...

    Text Solution

    |

  16. The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0....

    Text Solution

    |

  17. The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

    Text Solution

    |

  18. Let u-=a x+b y+a b3=0,v-=b x-a y+b a3=0,a ,b in R , be two straight l...

    Text Solution

    |

  19. Two sides of a triangle are parallel to the coordinate axes. If the ...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |