Home
Class 11
MATHS
Line segment AB of fixed lengh c slides ...

Line segment AB of fixed lengh c slides between coordinate axes such that its ends A and B lie on the axes. If O is origin and rectangle OAPB is completed, then show that the locus of the foot of the perpendicular drawn from P to AB is `x^((2)/(3)) + y^((2)/(3)) = c^((2)/(3)).`

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

The circle A and B of a line segment of constant length c unit slides upon the fixex rectangular axes OX and OY. If P be a point on the plane such that OAPB is a rectangle, then show that locus of the foot of the perpendicular drawn from P to AB is x^(2//3)+ y^(2//3)=c^(2//3) .

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

The locus of the foot of perpendicular drawn from the centre of the ellipse x^(2)+3y^(2)=6 on any tangent to it is-

A variable line makes intercepts on the co-ordinate axes , the sum of whose squares is constant and equal to k^2 . Show that the locus of the foot of the perpendicular from the origin to this line is (x^2+ y^2)^2 (x^(-2)+ y^(-2))=k^2 .

Find the foot of perpendicular drawn from the point (2, 2) to the line 3x - 4y + 5 = 0

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

A rod of length k slides in a vertical plane, its ends touching the coordinate axes. Prove that the locus of the foot of the perpendicular from the origin to the rod is (x^2+y^2)^3=k^2x^2y^2dot

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is

The coordinates of the foot of the perpendicular drawn from the point A(2, 4, -1) on the line (x+5)/(1)=(y+3)/(4)=(z-6)/(-9) are -

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. If P is a point (x,y) on the line y=-3x such that P and the point (3...

    Text Solution

    |

  2. If the points (1,2) and (3, 4) are on the opposite side of the line 3x...

    Text Solution

    |

  3. Line segment AB of fixed lengh c slides between coordinate axes such t...

    Text Solution

    |

  4. All points lying inside the triangle formed by the points (1,3),(5,0)a...

    Text Solution

    |

  5. The equation to the straight line passing through the point (a "cos"^(...

    Text Solution

    |

  6. The equation of a straight line on which the length of perpendicular ...

    Text Solution

    |

  7. The number of integral values of m for which the x-coordinate of the p...

    Text Solution

    |

  8. If the equation of base of an equilateral triangle is 2x-y=1 and the v...

    Text Solution

    |

  9. The equation of straight line passing through (-a ,0) and making a tr...

    Text Solution

    |

  10. The line P Q whose equation is x-y=2 cuts the x-axis at P ,a n dQ is (...

    Text Solution

    |

  11. If the equation of the locus of a point equidistant from the points (a...

    Text Solution

    |

  12. If the extremities of the base of an isosceles triangle are the points...

    Text Solution

    |

  13. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n ...

    Text Solution

    |

  14. The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A ...

    Text Solution

    |

  15. A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4/...

    Text Solution

    |

  16. A pair of perpendicular straight lines is drawn through the origin f...

    Text Solution

    |

  17. If the vertices Pa n dQ of a triangle P Q R are given by (2, 5) and (4...

    Text Solution

    |

  18. Given A=(1,1) and A B is any line through it cutting the x-axis at Bdo...

    Text Solution

    |

  19. The straight lines 4a x+3b y+c=0 passes through which point? , where a...

    Text Solution

    |

  20. The line parallel to the x-axis and passing through the intersection o...

    Text Solution

    |