Home
Class 11
MATHS
Let the equation ax^(2)+2hxy+2gx+2fy+c=0...

Let the equation `ax^(2)+2hxy+2gx+2fy+c=0` represent a pair of parallel lines. Prove that the equation of the line midway between the two parallel lines is `hx+by+f=0`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise ADDITIONAL SOLVED EXAMPLES|7 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE - 4.1 (VERY SHORT ANSWER QUESTIONS)|14 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|15 Videos

  • MULTIPLE PRODUCT OF VECTORS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|62 Videos

  • PERIODICITY AND EXTEME VALUES

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE) LEVEL-I(MAIN) Extreme values ( Single answer type questions )|23 Videos

Similar Questions

Explore conceptually related problems

If the equation 9x^(2)+24xy+by^(2)-12x+2fy-12=0 represents a pair of parallel lines, the f=

The equation ax^(2)+2hyx+by^(2)+2gx+2ry+c=0 represents a pair of parallel lines if (a)/(h)=(h)/(b)=

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that h^2=ab .

If the equation 2xy + gx + fy + 5 = 0 repre sents a pair of lines, then fg=

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that af^2=bg^2 .

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines then sqrt([q^2-ac/f^2-bc])=

The equation ax^(2)-24xy+16y^(2)+2gx+16y+c=0 represents a pair of parallel straight lines. Match the list-I to list-II.

AAKASH SERIES-PAIR OF STRAIGHT LINES-SOLVED EXAMPLES
  1. The figure formed by the pairs of lines 3x^(2)+10xy+3y^(2)=0 and 3x^(2...

    Text Solution

    |

  2. If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equi...

    Text Solution

    |

  3. Let the equation ax^(2)+2hxy+2gx+2fy+c=0 represent a pair of parallel ...

    Text Solution

    |

  4. IF the pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 int...

    Text Solution

    |

  5. If two of the sides of a parallelogram are represented by ax^2+2hxy+by...

    Text Solution

    |

  6. Find the equation to the pair of lines joining the origin to the point...

    Text Solution

    |

  7. Show that the pair of lines joining the origin to the points of the in...

    Text Solution

    |

  8. The chords of the curve 3x^(2)-y^(2)-2x+4y=0 subtend a right angle at ...

    Text Solution

    |

  9. Find the equation of the pair of lines throughh the origin and forming...

    Text Solution

    |

  10. Show that the lines x^(2)+16xy-11y^(2)=0 form an equilateral triangle ...

    Text Solution

    |

  11. If (alpha, beta) is the centroid of the triangle, whose sides are ax^(...

    Text Solution

    |

  12. The straight line lx+my+n=0 bisects and angle between the pair of line...

    Text Solution

    |

  13. Two equal sides of an isoceles triangle are given by 7x-y+3=0 and x+y-...

    Text Solution

    |

  14. Show that the product of the perpendicular from (alpha,beta) to the pa...

    Text Solution

    |

  15. If the pair of lines ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0 form ...

    Text Solution

    |

  16. If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equi...

    Text Solution

    |

  17. Let the equation ax^(2)+2hxy+2gx+2fy+c=0 represent a pair of parallel ...

    Text Solution

    |

  18. IF the pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 int...

    Text Solution

    |

  19. If two of the sides of a parallelogram are represented by ax^2+2hxy+by...

    Text Solution

    |

  20. Find the equation to the pair of lines joining the origin to the point...

    Text Solution

    |