Home
Class 11
MATHS
If the equation ax^2 + 2hxy + by^2 + 2gx...

If the equation `ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0` represents a pair of parallel lines, prove that
The distance between them is `2sqrt((g^2 - ac)/(a(a + b)))`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos
  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

Similar Questions

Explore conceptually related problems

If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pair of parallel lines, prove that a/h = h/b = g/f

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, then the distance between them is

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

The equation of second degree x^2 + 2sqrt2 xy + 2y^2 + 4x + 4 sqrt2 y + 1 = 0 represents a pair of straight lines, the distance between them is :

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, prove that h=sqrt(ab) and gsqrtb=fsqrta or (h=-sqrt(ab)and gsqrtb=-fsqrta)

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0 .

The equation x^2+y^2+2gx+2fy+c=0 represents a point -circle when

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. Find the condition that two of the three lines represented by ax^3+bx^...

    Text Solution

    |

  2. If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of para...

    Text Solution

    |

  3. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pa...

    Text Solution

    |

  4. prove that the product of the perpendiculars drawn from the point (x1,...

    Text Solution

    |

  5. The orthocentre of a triangle whose vertices are (0,0),(sqrt3,0) and (...

    Text Solution

    |

  6. The image of the point (3,8) with respect to the line x+3y=7 is

    Text Solution

    |

  7. The equations of the lines representing the sides of a triangle are 3x...

    Text Solution

    |

  8. The point (4,1) undergoes the following three transformations successi...

    Text Solution

    |

  9. A is (a,0) and B is (-a,0). If P is a point such that anglePAB - angle...

    Text Solution

    |

  10. The points (-a,-b).(0,0),(a,b) and (a^2, ab) are

    Text Solution

    |

  11. The medians AD and BE of a triangle ABC with vertices A(0, b), B(0, 0)...

    Text Solution

    |

  12. The vertices of a rhombus taken in order are (2,-1), (3,4), (-2,3), th...

    Text Solution

    |

  13. The coordinates of the point P on the lines 2x+3y+1=0, such that |PA-P...

    Text Solution

    |

  14. One vertex of the equilateral triangle with centroid at the origin and...

    Text Solution

    |

  15. If t1, t2 and t3 are distinct, the points (t1, 2at1+at1^3), (t2,2at2+a...

    Text Solution

    |

  16. If (-6,-4), (3,5),(-2,1) are the vertices of a parallelogram, then rem...

    Text Solution

    |

  17. A line passing through the point P(4,2) meets the x and y-axis at A an...

    Text Solution

    |

  18. If P-=(1,0), Q-=(-1, 0), R-=(2,0) are three given points, then the loc...

    Text Solution

    |

  19. A straight line segment AB of length 'a' moves with its ends on the ax...

    Text Solution

    |

  20. Let A be any variable point on the X-axis and B the point (2,3). The p...

    Text Solution

    |