Home
Class 11
MATHS
Show that the diagonals of the parallelo...

Show that the diagonals of the parallelogram whose sides are `l x+m y+n=0,l x+m y+n^(prime)=0,m x+l y+n=0` and `m x+l y+n^(prime)=0` include an angle `pi//2` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THE CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos

  • TRANSFORMATION FORMULAE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the circle which circumscribes the triangle formed by the lines x=0,\ y=0\ a n d\ l x+m y=1.

If the diagonals of the quadrilateral formed by lines l_1x+m_1y+n_1=0,l_2x+m_2y+n_2=0,l_1x+m_1y+n_1'=0 l_2x+m_2y+n_2'=0,are perpendicular, then value of l_1^2-l_2^2+m_1^2-m_2^2dot

Show that the equation of the circle which touches the coordinates axes whose centre lies on the line l x+m y+n=0\ i s\ (l+m)^2 (x^2 + y^2 )+2n(x+y)(l+m)+n^2=0.

If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 sq. units, then, a) l,m,n are in G.P b) l,n,m are in G.P. c) lm=n d) ln=m

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2-0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

The angle between the lines whose direction cosines are given by the equatios l^2+m^2-n^2=0, m+n+l=0 is

Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0a n d2//m+2n l-m n=0.

Show that the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent if l+m+n=0

RD SHARMA ENGLISH-THE STRAIGHT LINES -All Questions
  1. Find the values of alpha so that the point P(alpha^2,alpha) lies insid...

    Text Solution

    |

  2. Prove that the area of the parallelogram formed by the lines a1x+b1y+c...

    Text Solution

    |

  3. Show that the diagonals of the parallelogram whose sides are l x+m y+n...

    Text Solution

    |

  4. Find the ratio in which the line 3x+4y+2=0 divides the distance betwee...

    Text Solution

    |

  5. Prove that the area of the parallelogram formed by the lines xcosalpha...

    Text Solution

    |

  6. Find the equation of the perpendicular bisector of the line segment ...

    Text Solution

    |

  7. The vertices of a triangle are A(10 ,4),B(-4,0)a n dC(-2, 8)dot Find t...

    Text Solution

    |

  8. Two sides of a square lie on the lines x+y=1a n dx+y+2=0. What is its ...

    Text Solution

    |

  9. Prove that the line 5x-2y-1=0 is mid-parallel ot the lines 5x-2y-9=0a ...

    Text Solution

    |

  10. Find the equation of a line that has y - intercept 4 and is perpendic...

    Text Solution

    |

  11. P1, P2 are points on either of the two line y-sqrt(3)|x|=2 at a distan...

    Text Solution

    |

  12. Find the equation of a line has y-i n t ercept is -4 and is parallel ...

    Text Solution

    |

  13. Find the equation of a line passing through (1,2) and making angle of ...

    Text Solution

    |

  14. The vertices of a triangle are A(x1, x1tantheta1),B(x2, x2tantheta2)a ...

    Text Solution

    |

  15. Find the equation of a line which is parallel to y-axis and passes th...

    Text Solution

    |

  16. Find the equation of a line which is equidistant from the lines x=4 a ...

    Text Solution

    |

  17. Find the equation of a straight line which makes an angle of tan^(-1)s...

    Text Solution

    |

  18. The equation of the base of an equilateral triangle is x+y=2 and its v...

    Text Solution

    |

  19. find the slope of a line whose inclination to the positive directioin ...

    Text Solution

    |

  20. What can be said regarding a line if its slope is i. positive ii. zero...

    Text Solution

    |