Home
Class 11
MATHS
A point moves so that the sum of the squ...

A point moves so that the sum of the squares of the perpendiculars let fall from it on the sides of an equilateral triangle is constant. Prove that its locus is a circle.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

A straight line moves so that the product of the length of the perpendiculars on it from two fixed points is constant. Prove that the locus of the feet of the perpendiculars from each of these points upon the straight line is a unique circle.

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2, 1) is always 6. Then its locus is

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2,1) is always 6. Then its locus is

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6 . Then its locus is _

Prove that the sum of the perpendiculars drawn from any interior point of an equilateral triangle to its sides then sum of three perpendiculars is equal to the altitude of the triangle.

A point moves in such a manner that the sum of the squares of its distances from the origin and the point (2, -3) is always 19. Show that the locus of the moving point is a circle. Find the equation to the locus.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2...

    Text Solution

    |

  2. Find the center of the smallest circle which cuts circles x^2+y^2=1 an...

    Text Solution

    |

  3. A point moves so that the sum of the squares of the perpendiculars let...

    Text Solution

    |

  4. From a point P on the normal y=x+c of the circle x^2+y^2-2x-4y+5-lambd...

    Text Solution

    |

  5. The circle x^2+y^2-4x-4y+4=0 is inscribed in a variable triangle O A B...

    Text Solution

    |

  6. The line 9x+y-18=0 is the chord of contact of the point P(h , k) wit...

    Text Solution

    |

  7. A circle x^2+y^2+4x-2sqrt(2)y+c=0 is the director circle of the circle...

    Text Solution

    |

  8. Tangents are drawn to the circle x^2+y^2=9 at the points where it is ...

    Text Solution

    |

  9. Find the length of the chord of contact with respect to the point on ...

    Text Solution

    |

  10. The distance between the chords of contact of the tangent to the circl...

    Text Solution

    |

  11. If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find ...

    Text Solution

    |

  12. Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 an...

    Text Solution

    |

  13. Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that ...

    Text Solution

    |

  14. Find the equation of the chord of the circle x^2+y^2=9 whose middle po...

    Text Solution

    |

  15. Find the circle of minimum radius which passes through the point (4, 3...

    Text Solution

    |

  16. A variable chord is drawn through the origin to the circle x^2+y^2-2a ...

    Text Solution

    |

  17. The radius of the tangent circle that can be drawn to pass through the...

    Text Solution

    |

  18. Find the equation of the chord of the circle x^2+y^2=a^2 passing throu...

    Text Solution

    |

  19. If the lines 2x-3y-5=0 and 3x-4y=7 are diameters of a circle of area 1...

    Text Solution

    |

  20. Find the middle point of the chord of the circle x^2+y^2=25 intercepte...

    Text Solution

    |