Home
Class 12
MATHS
Show that the area of the triangle forme...

Show that the area of the triangle formed by the lines `y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0 " is " ((c_(1) - c_(2))^(2))/(2|m_(1) - m_(2)|)`

A

`a_(1)^(1)+a_(2)^(2)+b_(1)^(2)-b_(2)^(2)`

B

`(1)/(2)(a_(1)^(2)+a_(2)^(2)+b_(1)^(2)+b_(2)^(2))`

C

`sqrt(a_(1)^(2)+b_(1)^(2)-a_(2)^(2)-b_(2)^(2))`

D

`(1)/(2)(a_(2)^(2)+b_(2)^(2)-a_(1)^(2)-b_(1)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|53 Videos

  • STATISTICS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|40 Videos

  • THREE DIMENSIONAL GEOMETRY

    NEW JOYTHI PUBLICATION|Exercise Objective|36 Videos

Similar Questions

Explore conceptually related problems

If three lines whose equations are y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " m_(3) x + c_(3) are concurrent, then show that m_(1) (c_(2) - c_(3)) + m_(2) (c_(3) - c_(1)) + m_(3) (c_(1) - c_(2)) = 0 .

The area of the triangle formed by the lines y=a x ,x+y-a=0 , and the y-axis to (a) 1/(2|1+a|) (b) 1/(|1+a|) (c) 1/2|a/(1+a)| (d) (a^2)/(2|1+a|)

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

If y = sin (m sin^(-1) x), prove that (1 - x^2)y_2 -xy_1 + m^2 y = 0

The line a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 are perpendicular if:

Show that y = sin ( m sin^(-1)x) is a solution of the differential equation (1 - x^(2)) y '' + xy' + m^(2) y = 0

Choose the odd one out (1) y^(2) = 4ax (2) c= a/m (3) c^(2) = a^(2(1+m^(2))) (4) (a/m^(2) , (2a)/m)

if x,y and z are not all zero and connected by the equations a_(1)x+b_(1)y+c_(1)z=0,a_(z)x+b_(2)y+c_(2)z=0 and (p_(1)+lambdaq_(1))x+(p_(2)+lambdaq_(2))y+(p_(3)+lambdaq_(3))z=0 show that lambda =-|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(p_(1) ,, p_(2),,p_(3)):}|-:|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(q_(1) ,, q_(2),,q_(3)):}|

The line y = 2x + c touches the ellipse (x^2)/(16) + (y^2)/(4) = 1 if c is equal to

NEW JOYTHI PUBLICATION-STRAIGHT LINES-QUESTIONS FROM COMPETITIVE EXAMS
  1. A square of side a lies above the x-axis and has one vertex at the or...

    Text Solution

    |

  2. If the pairs of straight lines x^(2) - 2pxy-y^(2)=0 and x^(2) – 2qxy ...

    Text Solution

    |

  3. Locus of centroid of the triangle whose vertices are (a cost, a sint)...

    Text Solution

    |

  4. Show that the area of the triangle formed by the lines y = m(1) x + c(...

    Text Solution

    |

  5. Let A (2, -3) and B (-2, 1) be vertices of a triangle ABC. If the cen...

    Text Solution

    |

  6. The equation of the straight line passing through the point (4, 3) an...

    Text Solution

    |

  7. If the sum of the slopes of the lines given by x^(2) – 2cxy – 7y^(2) ...

    Text Solution

    |

  8. If one of the lines given by 6x^(2) - xy + 4cy^(2) = 0 is 3x + 4y = 0...

    Text Solution

    |

  9. The line parallel to the x-axis and passing through the intersection ...

    Text Solution

    |

  10. If non-zero numbers a, b, c are in H.P., then the straight line (x)/(...

    Text Solution

    |

  11. If a vertex of a triangle is (1, 1) and the mid points of two sides t...

    Text Solution

    |

  12. If the pair of lines ax^(2) + 2(a+b)xy + by^(2) = 0 lie along diamete...

    Text Solution

    |

  13. A straight line through the point A(3, 4) is such that its intercept ...

    Text Solution

    |

  14. In are ellispe , the distance between its foci is 6 and its minor axi...

    Text Solution

    |

  15. If (a, a^(2)) falls inside the angle made by the lines y=(x)/(2), x g...

    Text Solution

    |

  16. The equation of a tangent to the parabola y^(2) = 8x is y = x + 2. Th...

    Text Solution

    |

  17. Let A(h, k), B (1, 1) and C(2, 1) be the vertices of a right angled t...

    Text Solution

    |

  18. Let P=(-1, 0), Q=(0,0) and R=(3, 3sqrt3) be three points. The equatio...

    Text Solution

    |

  19. If one of the lines of my^(2) + (1 - m^(2))xy - mx^(2) = 0 is a bisect...

    Text Solution

    |

  20. The perpendicular bisector of the line segment joining P(1, 4) and Q(...

    Text Solution

    |