Home
Class 11
MATHS
The vertices of a triangle are [a t1t2,a...

The vertices of a triangle are `[a t_1t_2,a(t_1 +t_2)]`, `[a t_2t_3,a(t_2 +t_3)]`, `[a t_3t_1,a(t_3 +t_1)]` Then the orthocenter of the triangle is (a) `(-a, a(t_1+t_2+t_3)-at_1t_2t_3)` (b) `(-a, a(t_1+t_2+t_3)+at_1t_2t_3)` (c) `(a, a(t_1+t_2+t_3)+at_1t_2t_3)` (d) `(a, a(t_1+t_2+t_3)-at_1t_2t_3)`

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 of a triangle are [at_1t_2, a(t_1+t_2)],[at_2t_3,a(t_2+t_3)],[at_3t_1,a(t_3+t_1)] Find the orthocentre of the triangle.

If the Verticesof a triangle are P(at_1,a/t_1) , Q(at_2,a/t_2) and R(at_3,a/t_3) Show that the orthocentre of the triagle lies on xy = a^2 .

The coordinates of the vertices of a triangle are [at_(1)t_(2),a(t_(1)+t_(2))],[at_(2),t_(3),a(t_(2)+t_(3))] and [at_(3)t_(1),t_(3)+t_(1))] . Find the coordinates of the ortocentre of the triangle.

If t_1,t_2 and t_3 are distinct, the points (t_1, 2at_1 + at_1^3), (t_2, 2at_2 + at_2^3), (t_3, 2at_3 +at_3^3) are collinear then show that t_1+t_2+t_3=0 .

The slope of the tangent to the curve x= 3t^(2) +1 , y=t^(3)-1 at x=1 is-

If t_1, t_2 and t_3 are distinct, the points (t_1, 2at_1+at_1^3), (t_2,2at_2+at_2^3) and (t_3,2at_3+at_3^3) are collinear if

If the normals at P(t_(1))andQ(t_(2)) on the parabola meet on the same parabola, then (A) t_(1)t_(2)=-1 (B) t_(2)=-t_(1)-(2)/(t_(1)) (C) t_(1)t_(2)=1 (D) t_(1)t_(2)=2

Prove that the area of the triangle whose vertices are (t ,t-2),(t+2,t+2), and (t+3,t) is independent of tdot

Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9 .

Find y_2 in each of the following cases: x=a(t+1/t) , y=a(t-1/t)

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. OX and OY are two coordinate axes. On OY is taken a fixed point P(0,c)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. In Delta ABC, the coordinates of B are (0,0) AB=2,angleABC=pi//3, and ...

    Text Solution

    |

  13. If in triangle ABC, A=(1, 10), circumcentre=(-1/3, 2/3) and orthocentr...

    Text Solution

    |

  14. Find The orthocenter of the triangle formed by (0,0),(8,0),(4,6)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. P and Q are points on the line joining A(-2,5) and B(3,1) such that AP...

    Text Solution

    |

  20. The point (4,1) undergoes the following three transformations successi...

    Text Solution

    |