Home
Class 11
MATHS
Prove that the length of perpendiculars ...

Prove that the length of perpendiculars from points 'P(m^2,2m) Q (mn ,m+n) and R(n^2,2n)' to the line `x cos^2theta+ysinthetacostheta+sin^2theta=0` are in G.P.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THE CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos

  • TRANSFORMATION FORMULAE

    RD SHARMA ENGLISH|Exercise All Questions|145 Videos

Similar Questions

Explore conceptually related problems

The lengths of the perpendiculars from the points (m^(2), 2m), (mn, m+n) and (n^(2), 2n) to the line x+sqrt3y+3=0 are in

Prove that the lengths of the perpendiculars from the points (m^2,2m),(m m^(prime),m+m^(prime)), and (m^(prime2),2m^(prime)) to the line x+y+1=0 are in GP.

Prove that the lengths of the perpendiculars from the points (m^2,2m),(m m^(prime),m+m^(prime)), and (m^('2),2m^(prime)) to the line x+y+1=0 are in GP.

If p_(1),p_(2),p_(3) be the length of perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^('2),2m') respectively on the line xcosalpha+ysinalpha+(sin^(2)alpha)/(cosalpha)=0 then p_(1),p_(2),p_(3) are in:

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

If p and q are the lengths of perpendiculars from the origin to the lines xcostheta-ysintheta=kcos2theta and xsec""theta+y" cosec"""theta=""k , respectively, prove that p^2+4q^2=k^2 .

If (2^n+1)theta=pi then 2^n costheta cos2theta cos2^2 theta .......cos 2^(n-1) theta=

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

If p and q are respectively the perpendiculars from the origin upon the striaght 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 t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

RD SHARMA ENGLISH-THE STRAIGHT LINES -All Questions
  1. Find the equation of the straight lines each of which passes through ...

    Text Solution

    |

  2. The equation of straight line which passes through the point (-4,3) su...

    Text Solution

    |

  3. Prove that the length of perpendiculars from points 'P(m^2,2m) Q (mn ,...

    Text Solution

    |

  4. The equation of the base of an equilateral triangle is x+y-2=0 and the...

    Text Solution

    |

  5. Find the equations of lines passing through the point (1,0) and a dist...

    Text Solution

    |

  6. Find the coordinates of a point on x+y+3=0, whose distance from x+2y+2...

    Text Solution

    |

  7. A point moves such teat its distance from the point (4,0) is half that...

    Text Solution

    |

  8. Find the locus of a point which moves in such away that the square of ...

    Text Solution

    |

  9. Find the equation of the straight line on which the length of the pe...

    Text Solution

    |

  10. Find the equation of the straight line upon which the length of the ...

    Text Solution

    |

  11. A line forms a triangle of area 54sqrt(3)s q u a r e units with the co...

    Text Solution

    |

  12. A straight canal is 4 1/2m i l e s from a place and the shortest route...

    Text Solution

    |

  13. Find the equation of the line on which the length of the perpendicular...

    Text Solution

    |

  14. Find the equation of the straight line on which the length of the p...

    Text Solution

    |

  15. Find the equation of a straight line on which the perpendicular from ...

    Text Solution

    |

  16. The slope of a straight line through A(3,2)i s3//4 Find the coordinate...

    Text Solution

    |

  17. Find the equation of the line through the point A(2,3) and making an a...

    Text Solution

    |

  18. If the straight line through the point (3,4) makes an angle pi/6 with ...

    Text Solution

    |

  19. The angle between the diagonals of a quadrilateral formed by the line...

    Text Solution

    |

  20. Find the equation of two straight lines which are parallel to x+7y+2=0...

    Text Solution

    |