Home
Class 11
MATHS
If p and q are the lengths of perpendic...

If `p` and `q` are the lengths of perpendicular from the origin to the line `xcos(theta)-ysin(theta)=kcos(2theta)` and` xsec(theta)+ycosec(theta)=k` respectively , then prove that `p^2+4q^2=k^2`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

  • STATISTICS

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|7 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|10 Videos

Similar Questions

Explore conceptually related problems

If p and q are the lengths of perpendicular from the origin to the line x cos(theta)-y sin(theta)=k cos(2 theta) and x sec(theta)+y cos ec(theta)=k respectively,then prove that p^(2)+4q^(2)=k^(2)

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta-y sin theta=k cos2 theta and x sec theta+y csc theta=k respectively,prove that quad p^(2)+4q^(2)=k^(2)

If p_(1) and p_(2) are the lengths of the perpendicular form the orgin to the line x sec theta+y cosec theta=a and xcostheta-y sin theta=a cos 2 theta respectively then prove that 4p_(1)^(2)+p_(2)^(2)=a^(2)

If sin theta + cos theta = p and sec theta + "cosec"theta = q , then prove that q(p^(2)-1) = 2p .

If p and p_1 be the lengths of the perpendiculars drawn from the origin upon the straight lines x sin theta + y cos theta = 1/2 a sin 2 theta and x cos theta - y sin theta = a cos 2 theta , prove that 4p^2 + p^2_1 = a^2 .

Distance of the lines xcosectheta+ysectheta=kcot2theta and xsintheta+ycostheta=ksin2theta from origin is p and q respectively then

If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = acos 2 theta , then 4p^(2) + q^(2) is equal to

If sin theta+cos theta=p and sec theta+cos ec theta=q find q(p^(2)-1)=

NAGEEN PRAKASHAN-STRAIGHT LINES-Exercise
  1. Find the distance between the parallel lines x+4sqrt(3)y+10=0 and x+4s...

    Text Solution

    |

  2. Find the relation between a and b if the lines 3x-by+5=0 and ax+y=2 pa...

    Text Solution

    |

  3. If p and q are the lengths of perpendicular from the origin to the li...

    Text Solution

    |

  4. Show that the distance between the parallel lines ax+by+c=0 and k(ax+b...

    Text Solution

    |

  5. (i) If the length of perpendicular from origin to the line ax+by+a+b=0...

    Text Solution

    |

  6. The equations of sides AB, BC and AC of DeltaABC are respectively y=x,...

    Text Solution

    |

  7. If p is the length of perpendicular from the origin to the line whose...

    Text Solution

    |

  8. Find the coordinates of the incentre and centroid of the triangle whos...

    Text Solution

    |

  9. Find the co-ordinates of the circumcentre of a triangle whose vertices...

    Text Solution

    |

  10. Find the co-ordinates of the orthocentre of a triangle whose vertices ...

    Text Solution

    |

  11. The equation of one diagonal of a square is 2x+y=6 and its one vertex ...

    Text Solution

    |

  12. The co-ordinates of the vertex of an equilateral triangle are (2,-1) a...

    Text Solution

    |

  13. A ray of light is sent along the line x-2y-3=0 upon reaching the line ...

    Text Solution

    |

  14. show that the equation of the straight line through the origin making ...

    Text Solution

    |

  15. Show that the straight lines given by (2+k)x+(1+k)y=5+7k for different...

    Text Solution

    |

  16. Find the equation of a line passing through the point of intersection ...

    Text Solution

    |

  17. Find the equation of a line passing through the point of intersection ...

    Text Solution

    |

  18. Find the equation of line passing through the point of intersection of...

    Text Solution

    |

  19. Find the equation of a line passing through the point of intersection ...

    Text Solution

    |

  20. Find the equation of a line passing through the point of intersection ...

    Text Solution

    |