Home
Class 11
MATHS
prove that the product of the perpendicu...

prove that the product of the perpendiculars drawn from the point `(x_1, y_1)` to the pair of straight lines `ax^2+2hxy+by^2=0` is `|(ax_1^2+2hx_1y_1+by_1^2)/sqrt((a-b)^2+4h^2)|`

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

Find the coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

find the length of the perpendicular drawn from the point (2,1,-1) on the line x - 2y + 4z = 9

The pair of straight lines x+2y-1=0,x+2y-5=0 are.

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

Show that the product of the perpendiculars drawn from the two points (+-sqrt(a^(2)-b^(2)),0) upon the straight line (x)/(a)costheta+(y)/(b)sintheta=1 is b^(2)

Product of the perpendiculars from (alpha, beta) to the lines ax^2+2hxy+by^2=0 is

Find the lengths of the tangents drawn from the point. (x_(1),y_(1)) to the circle x^(2)+y^(2)+2x=0

Find the lengths of the tangents drawn from the point. (-1,1) to the circle x^(2)+y^(2)-2x+4y+1=0

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2),0) and (-sqrt(a^2-b^2),0) to the line x/a costheta + y/b sintheta=1 is b^2 .

The angle between the two straight line of a pair of straight line x^2 - y^2 - 2y - 1 = 0 is

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. If theta is the angle between the lines givne by the equation 6x^(2)...

    Text Solution

    |

  2. The dis tance of a point (x(1),y(1)) from each of the two straight li...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the area enclosed by the graph of x^2y^2-9x^2-25 y^2+225=0.

    Text Solution

    |

  5. Show that the pairs of straight lines 2x^(2)+6xy+y^(2)=0 and 4x^(2)18x...

    Text Solution

    |

  6. Show that the equation of the pair of lines bisecting the angles betwe...

    Text Solution

    |

  7. Find the angle between the straight lines joining the origin to the po...

    Text Solution

    |

  8. Through a point A on the x-axis, a straight line is drawn parallel to ...

    Text Solution

    |

  9. Find the equation of two straigh lines whose combined equation is 6x^(...

    Text Solution

    |

  10. Does equation x^(2)+2y^(2)-2sqrt(3)x-4y+5=0 satisfies the condition ...

    Text Solution

    |

  11. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

    Text Solution

    |

  12. Find the distance between the pair of parallel lines x^(2)+4xy+4...

    Text Solution

    |

  13. If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the ...

    Text Solution

    |

  14. Find the equation of two straigh lines whose combined equation is 6x^(...

    Text Solution

    |

  15. If the component lines whose combined equation is px^(2)-qxy-y^(2)=0 m...

    Text Solution

    |

  16. Find the joint equation of pair of lines which passes through origin a...

    Text Solution

    |

  17. If the sum of the slopes of the lines given by x^(2)-2cxy-7y^(2)=0 is...

    Text Solution

    |

  18. The distance between the two lines represented by the equation 9x^2-2...

    Text Solution

    |

  19. The gradient of one of the lines ax^2+2hxy+by^2=0 is twice that of the...

    Text Solution

    |

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

    Text Solution

    |