Home
Class 11
MATHS
Show that product of the perpendicular d...

Show that product of the perpendicular distances from origin to pair of lines represented by `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` is `(|c|)/(sqrt((a-b)^(2)+4h^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`(|c|)/(sqrt((a-b)^(2)4h^(2)))`
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 pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis, then show that 2fgh-bg^(2)-ch^(2)=0

If theta is the angle between the pair of lines represented by ax^2 + 2hxy + by^2 = 0 , then prove that cos theta= (|a+b|)/(sqrt((a-b)^2 + 4h^2))

Show that the product of the perpendicular from (alpha,beta) to the pair of lines S-= ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (|aalpha^(2)+2halphabeta+2galpha+2fbeta+c|)/(sqrt((a-b)^(2)+4h^(2))) Hence or otherwise find the product of the perpendicular from the origin

Show that the product of perpendicular from (alpha, beta) to the pair of lines ax^2 + 2hxy + by^2= 0 is |(aalpha^2 + 2h alpha beta + b beta^2)/(sqrt((a-b)^2 - (2h)^2))|

If ax ^(2) + 2kxy + by ^(2) + 2gx + 2fy + c =0 then (dy)/(dx) =

If the slope of one of the lines represented by ax^(2) + 2hxy + by^(2) = 0 is the square of the other, then (a+b)/h+(8h^(2))/(ab)

AAKASH SERIES-PAIR OF STRAIGHT LINES-SOLVED EXAMPLES
  1. Find the value of lambda for which the equation lambdax^(2) - 10xy + 1...

    Text Solution

    |

  2. Prove that the equation 6x^(2)+xy-12y^(2)-14x+47y-40=0 and 14x^(2)+xy^...

    Text Solution

    |

  3. Show that product of the perpendicular distances from origin to pair o...

    Text Solution

    |

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

    Text Solution

    |

  5. The figure formed by the pairs of lines 3x^(2)+10xy+3y^(2)=0 and 3x^(2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |