Home
Class 11
MATHS
The vertices A,B, and C of a variable ri...

The vertices A,B, and C of a variable right triangle lie on a parabola `y^(2)=4x`. If the vertex B containing the right angle always remains at the point (1,2), then find the locus of the centroid of triangle ABC.

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

The vertices A ,Ba n dC of a variable right triangle lie on a parabola y^2=4xdot If the vertex B containing the right angle always remains at the point (1, 2), then find the locus of the centroid of triangle A B Cdot

An equilateral triangle inscribe a parabola y^2 = 4ax . such that oneof the vertex of the triangle lies on the vertex of the parabola-. Find the,length of,the each side. of the triangle:

If vertex A of triangle ABC is (3,5) and centroid is (-1,2) , then find the midpoint of side BC.

An equilateral triangle is inscribed in the parabola y^(2)=4ax , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

A right-angled triangle A B C is inscribed in parabola y^2=4x , where A is the vertex of the parabola and /_B A C=pi/2dot If A B=sqrt(5), then find the area of A B Cdot

An equilateral triangle is inscribed in the parabola y^2=4a x , such that one vertex of this triangle coincides with the vertex of the parabola. Then find the side length of this triangle.

If chord BC subtends right angle at the vertex A of the parabola y^(2)=4x with AB=sqrt(5) then find the area of triangle ABC.

Let A(2,-3) and B(-2,1) be the vertices of Delta A B Cdot If the centroid of the triangle moves on the line 2x+3y=1, then find the locus of the vertex Cdot

A variable line through the point P(2,1) meets the axes at a an d b . Find the locus of the centroid of triangle O A B (where O is the origin).

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Statement 1 : Slopes of tangents drawn from (4, 10) to the parabola ...

    Text Solution

    |

  2. Statement 1: The line joining the points (8,-8)a n d(1/2,2), which are...

    Text Solution

    |

  3. The vertices A,B, and C of a variable right triangle lie on a parabol...

    Text Solution

    |

  4. Show that the common tangents to the parabola y^2=4x and the circle x^...

    Text Solution

    |

  5. Consider a curve C : y^2-8x-2y-15=0 in which two tangents T1a n dT2 ar...

    Text Solution

    |

  6. Statement 1: The length of focal chord of a parabola y^2=8x making on ...

    Text Solution

    |

  7. Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabo...

    Text Solution

    |

  8. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

    Text Solution

    |

  9. If d is the distance between the parallel tangents with positive slop...

    Text Solution

    |

  10. If P(t^(2),2t),tin[0,2], is an arbitrary point on the parabola y^(2)=4...

    Text Solution

    |

  11. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

    Text Solution

    |

  12. If the locus of the middle of point of contact of tangent drawn to the...

    Text Solution

    |

  13. The minimum area of circle which touches the parabolas y=x^2+1 and y^2...

    Text Solution

    |

  14. Tangent is drawn to parabola y^(2)-2y-4x+5=0 at a point P which cuts t...

    Text Solution

    |

  15. The point of intersection of the tangents at the ends of the latus ...

    Text Solution

    |

  16. If the normals of the parabola y^2=4x drawn at the end points of its l...

    Text Solution

    |

  17. From a point A common tangents are drawn to a circle x^2 +y^2 = a^2/2 ...

    Text Solution

    |

  18. If two tangents drawn from a point P to the parabola y^2 = 4x are at r...

    Text Solution

    |

  19. Normals are drawn from the point P with slopes m(1),m(2)andm(3) to tha...

    Text Solution

    |

  20. Three normals are drawn from the point (c, 0) to the curve y^2 = x. Sh...

    Text Solution

    |