Home
Class 12
MATHS
If the quadrilateral formed by the lines...

If the quadrilateral formed by the lines `a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0` has perpendicular diagonals, then `b^2+c^2=b^('2)+c^('2)` `c^2+a^2=c^('2)+a^('2)` `a^2+b^2=a^('2)+b^('2)` (d) none of these

A

`b^(2)+c^(2)=b^(2)+c^(2)`

B

`c^(2)+a^(2)=c^(2)+a^(2)`

C

`a^(2)+b^(2)=a^(2)+b^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 3|17 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 4|15 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

Similar Questions

Explore conceptually related problems

If the quadrilateral formed by the lines ax+by+c=0,a'x+b'y+c=0,ax+by+c'=0,a'x+b'y+c'=0 has perpendicular diagonals,then (a)b^(2)+c^(2)=b^(prime2)+c^(2)(b)c^(2)+a^(2)=c^(2)+a^(prime2)(c)a^(2)+b^(2)=a^(2)=a^(2)+b^(2)(d) none of these

the diagonals of the parallelogram formed by the the lines a_(1)x+b_(1)y+c_(1)=0,a_(1)x+b_(1)y+c_(1)^(prime)=0,a_(2)x+b_(2)y+c_(1)=0,a_(2)x+b_(2)y+c_(1)^(prime) will be right angles if:

The angle between the lines a _(1) x + b_(1)y+c_(1) =0 and a _(2)x+ b_(2)y+c_(2)=o, is

|(bc,bcprime+bprime c, bprime c prime),(ca,ca prime+c prime a,c prime a prime),(ab, ab prime+a prime b,a prime b prime)| is equal to

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a ,b ,ca n da^(prime),b^(prime),c^(prime) respectively, prove that 1/(a^2)+1/(b^2)+1/(c^2)=1/(a^('2))+1/(b^('2))+1/(c^('2))

ARIHANT MATHS-THE STRAIGHT LINES-Exercise For Session 2
  1. The number of lines that are parallel to 2x + 6y -7= 0 and have an int...

    Text Solution

    |

  2. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

    Text Solution

    |

  3. Let the algebraic sum of the perpendicular distances from the points (...

    Text Solution

    |

  4. If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(pri...

    Text Solution

    |

  5. The area of the parallelogram formed by the lines 3x-4y + 1=0, 3x-4y +...

    Text Solution

    |

  6. Area of the parallelogram formed by the lines y = mx, y = mx + 1,y = n...

    Text Solution

    |

  7. The co-ordinates of a point on the line y = x where perpendicular di...

    Text Solution

    |

  8. A line passes through the point (2,2) and is perpendicular to the lin...

    Text Solution

    |

  9. If the point (1,2) and (34) were to be on the same side of the line 3x...

    Text Solution

    |

  10. The lines y = mx , y + 2x = 0 , y = 2x + k and y + mx = k form a rh...

    Text Solution

    |

  11. What are the points on the x-axis whose perpendicular distance from th...

    Text Solution

    |

  12. The three sides of a triangle are given by (x^2 - y^2)(2x+3y-6) = 0. I...

    Text Solution

    |

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

    Text Solution

    |

  14. If the point as (4,7) and (costheta,sintheta) , where 0<theta<pi , lie...

    Text Solution

    |

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

    Text Solution

    |

  16. If the area of the parallelogram formed by the lines 2x - 3y + a = 0 ,...

    Text Solution

    |

  17. A line L is a drawn from P(4,3) to meet the lines L-1a n dL2 given by ...

    Text Solution

    |

  18. The vertices of a triangleOBC are O(0,0) , B(-3,-1), C(-1,-3). Find th...

    Text Solution

    |