Home
Class 11
MATHS
O X and O Y are two coordinate axes. On ...

`O X` and `O Y` are two coordinate axes. On `O Y` a fixed point `P(0,c)` is taken and on `O X` any point `Q` is taken. On `P Q ,` an equilateral triangle is described, its vertex `R` being on the side of `P Q` away from `O` . Then prove that the locus of `R` is `y=sqrt(3)x-c`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Let P is a point on the line y+2x=2 and Q and R are two points on the line 3y+6x=3 . If the triangle PQR is an equilateral triangle, then its area (in sq. units) is equal to

A variable straight line is drawn from a fixed point O meeting a fixed circle in P and point Q is taken on this line such that OP.OQ is constant ,then locus of Q is

A straight lien is drawn from a fixed point O metting a fixed straight line P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.

A straight line is drawn from a fixed point O meeting a fixed straight line in P . A point Q is taken on the line OP such that OP.OQ is constant. Show that the locus of Q is a circle.

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

The coordinates of the point P are (-3,\ 2) . Find the coordinates of the point Q which lies on the line joining P and origin such that O P=O Q .

P is a point on the line y+2x=1, and Q and R are two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O PdotO Q=p^2 , then find the locus of the point Qdot

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5...

    Text Solution

    |

  2. If (x , y) and (x ,y) are the coordinates of the same point referred t...

    Text Solution

    |

  3. O X and O Y are two coordinate axes. On O Y a fixed point P(0,c) is t...

    Text Solution

    |

  4. Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of...

    Text Solution

    |

  5. The vertices of a triangle are [a t1t2,a(t1 +t2)], [a t2t3,a(t2 +t3)],...

    Text Solution

    |

  6. If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then the...

    Text Solution

    |

  7. The maximum area of the triangle whose sides a,b and c satisfy 0leqale...

    Text Solution

    |

  8. If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n...

    Text Solution

    |

  9. Let O-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that th...

    Text Solution

    |

  10. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

    Text Solution

    |

  11. The vertices A and D of square A B C D lie on the positive sides of x ...

    Text Solution

    |

  12. A light ray emerging from the point source placed at P(2,3) is reflect...

    Text Solution

    |

  13. If the origin is shifted to the point ((a b)/(a-b),0) without rotation...

    Text Solution

    |

  14. In A B C , the coordinates of B are (0,0),A B=2,/A B C=pi/3, and t...

    Text Solution

    |

  15. If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...

    Text Solution

    |

  16. A triangle ABC with vertices A(-1,0),B(-2,3/4) & C(-3,-7/6) has its or...

    Text Solution

    |

  17. In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0)...

    Text Solution

    |

  18. If the vertices of a triangle are (sqrt(5,)0) , (sqrt(3),sqrt(2)) , an...

    Text Solution

    |

  19. The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), a...

    Text Solution

    |

  20. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

    Text Solution

    |