Home
Class 11
MATHS
If on a given base B C , a triangle is d...

If on a given base `B C ,` a triangle is described such that the sum of the tangents of the base angles is `m ,` then prove that the locus of the opposite vertex `A` is a parabola.

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

If on a given base BC[B(0,0) and C(2,0)], a triangle is described such that the sum of the base angles is 4, then the equation of the locus of the opposite vertex A is parabola whose directrix is y=k. The value of k is _________ .

If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.

Having given the bases and the sum of the areas of a number of triangles which have a common vertex, show that the locus of the vertex is a straight line.

Answer any one : If in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then prove that the angle opposite to the first side will be a right angle.

In triangle ABC, base BC is fixed. Then prove that the locus of vertex A such that tan B+tan C= Constant is parabola.

The base of a triangle is divided into three equal parts. If t_1, t_2,t_3 are the tangents of the angles subtended by these parts at the opposite vertex, prove that (1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot

Prove that the locus of the center of the circle which touches the given circle externally and the given line is a parabola.

Tangents are drawn to the parabola at three distinct points. Prove that these tangent lines always make a triangle and that the locus of the orthocentre of the triangle is the directrix of the parabola.

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.

If the base angles of triangle are ((22)/(12))^@ and (112 1/2)^@ , then prove that the altitude of the triangle is equal to 1/2 of its base.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the values of alpha so that the point P(alpha^2,alpha) lies insid...

    Text Solution

    |

  2. The locus of the centre of a circle the touches the given circle exter...

    Text Solution

    |

  3. If on a given base B C , a triangle is described such that the sum of ...

    Text Solution

    |

  4. The parametric equation of a parabola is x=t^2+1,y=2t+1. Then find the...

    Text Solution

    |

  5. If the focus of a parabola is (2,3) and its latus rectum is 8, then fi...

    Text Solution

    |

  6. y^2+2y-x+5=0 represents a parabola. Find its vertex.

    Text Solution

    |

  7. Find equation of parabola which has axis parallel to y-axis and which ...

    Text Solution

    |

  8. Prove that the focal distance of the point (x ,y) on the parabola x^2-...

    Text Solution

    |

  9. Find points on the parabola y^(2)-2y-4x=0 whose focal length is 6.

    Text Solution

    |

  10. If the length of the common chord of circle x^2+y^2=4 and y^2=4(x-h) i...

    Text Solution

    |

  11. From a variable point p on line 2x−y-1=0 pair of tangents are draw...

    Text Solution

    |

  12. The locus of the middle points of the focal chords of the parabola, y^...

    Text Solution

    |

  13. If the distance of the point (h,2) from its chord of contact w.r.t. pa...

    Text Solution

    |

  14. TP and TQ are tangents to the parabola, y^(2)=4ax at P and Q. If the c...

    Text Solution

    |

  15. Find the locus of midpoint of normal chord of parabola y^(2)=4ax.

    Text Solution

    |

  16. If normal to the parabola y^2-4a x=0 at alpha point intersects the par...

    Text Solution

    |

  17. If the parabolas y^(2)=4axandy^(2)=4c(x-b) have a common normal other ...

    Text Solution

    |

  18. Find the angle made by a double ordinate of length 8a at the vertex of...

    Text Solution

    |

  19. The cable of a uniformly loaded suspension bridge hangs in the form of...

    Text Solution

    |

  20. If the chord of contact of tangents from a point P to the parabola y^2...

    Text Solution

    |