Home
Class 12
MATHS
If the circumcenter of an acute-angled t...

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points `(a^2+1,a^2+1)` and `(2a ,-2a),` then find the orthocentre.

A

`y-2ax=0`

B

`y-(a^(2)+1)x=0`

C

`y+x=0`

D

`(a-1)^(2)x-(a+1)^(2)y=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES AND PAIR OF STRAIGHT LINES

    DISHA PUBLICATION|Exercise EXERCISE 1: CONCEPT BUILDER|60 Videos
  • SETS

    DISHA PUBLICATION|Exercise EXERCISE-2 : CONCEPT APPLICATOR|30 Videos
  • THREE DIMENSIONAL GEOMETRY

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

If the circumcentre of a triangle lies at the point (a, a) and the centroid is the mid - point of the line joining the points (2a+3, a+4) and (a-4, 2a-3) , then the orthocentre of the triangle lies on the line

Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation 5x-3y=0 Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio 1:2

Find the distance of the point (1,-2,3) from the line joining the points (-1,2,5) and (2,3,4).

Find the distance of the point (1,2) from the mid-point of the line segment joining the points (6,8) and (2,4)

If point P(4,2) lies on the line segment joining the points A(2,1) and B(8,4) then :

If point P(4,2) lies on the line segment joining the points A(2,1) and B(8,4) then

Find the angle between the lines Joining the points (-1,2),(3,-5) and (-2,3),(5,0)

if the straight line joining the points (3,4) and (2,-1) be parallel to the line joining the points (a,-2) and (4,-a), find the value of a.

Find the angle between the line joining the points (1,-2), (3,2) and the line x+2y-7=0

A point with z-coordinate 6 lies on the line segment joining the points (2, 1, 2) and (6, 0, 8). Find the coordinates of the point.

DISHA PUBLICATION-STRAIGHT LINES AND PAIR OF STRAIGHT LINES-EXERCISE 2: CONCEPT APPLICATOR
  1. Let P Q R be a right-angled isosceles triangle, right angled at P(2,1)...

    Text Solution

    |

  2. The number of lines that are parallel to 2x + 6y -7= 0 and have an int...

    Text Solution

    |

  3. A vertex of an equileteral triangle is (2;3) and the equation of the o...

    Text Solution

    |

  4. The value of lambda for which the lines joining the point of intersect...

    Text Solution

    |

  5. For a gt b gt c gt 0 if the distance between (1,1) and the point of i...

    Text Solution

    |

  6. Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from parallelogram rhombus cyclic...

    Text Solution

    |

  7. Find the image of the point (4,-13) in the line 5x+y+6=0.

    Text Solution

    |

  8. If a pair of perpendicular straight lines drawn through the origin ...

    Text Solution

    |

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

    Text Solution

    |

  10. Given a family of lines a(2x +y+4) + b(x-2y-3)=0 .The number of lines ...

    Text Solution

    |

  11. If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0, represents a pair of straight ...

    Text Solution

    |

  12. The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0by t...

    Text Solution

    |

  13. Find the combined equation of the pair of lines through the point (1, ...

    Text Solution

    |

  14. A ray of light coming fromthe point (1, 2) is reflected at a point A o...

    Text Solution

    |

  15. Vertices of a variable triangle are (3, 4), (5 cos theta, 5 sin theta)...

    Text Solution

    |

  16. If the angle between the two lines represented by 2x^(2)+5xy+3y^(2)+6x...

    Text Solution

    |

  17. A line L intersects three sides BC, CA and AB of a triangle in P,Q,R r...

    Text Solution

    |

  18. The distance of the line 2x+y=3 from the point (-1,3) in the direction...

    Text Solution

    |

  19. If the circumcenter of an acute-angled triangle lies at the origin ...

    Text Solution

    |

  20. Given vertices A (1, 1),B(4, -2)&C(5, 5) of a triangle, find the equat...

    Text Solution

    |