Home
Class 12
MATHS
Given the base BC of the triangle ABC an...

Given the base BC of the triangle ABC and if `angleC-angleB=k,` a constant, show that the locus of the vertex A is a hyperbola.

Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    AAKASH SERIES|Exercise Exercise -I|47 Videos

  • HYPERBOLA

    AAKASH SERIES|Exercise Exercise -II|42 Videos

  • HYPERBOLA

    AAKASH SERIES|Exercise Exercise -5.3 (Short Answer Questions)|2 Videos

  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|167 Videos

Similar Questions

Explore conceptually related problems

Given the base of the triangle and the sum of tangent of base angles as a negative constant -k^(2) , show that the locus of the vertex of the triangle is a parabola.

Let A(2, -3) and B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x+3y=1 , then the locus of the vertex C is the line

Let A(2, -3),B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x+3y=1 , then locus of the vertex 'C' is the line

The inverse of "if in a triangle ABC, AB gt AC then angleC gt angleB " is

The inverse of "if in a triangle ABC, AB = AC then angleB = angleC " is

The converse of "if in a triangle ABC, AB gt AC then angleC gt angleB " is

The base of a triangle lies along the line x=a and is of length a. The area of the triangle is a^2. The locus of the third vertex is

What is the area of a triangle ABC when AB = BC=5cm and angleB=90^@ (In sq ems)?

A variable plane is at a constant distance 3p from the origin and meets the axes A, B and C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2)

AAKASH SERIES-HYPERBOLA-Additional Exercise
  1. The equation of the line passing throught the centre of a rectangular ...

    Text Solution

    |

  2. A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes...

    Text Solution

    |

  3. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

    Text Solution

    |

  4. Prove that the locus of the point of intersection of tangents at the e...

    Text Solution

    |

  5. Prove that the portion of the tangent of the rectangular hyperbola int...

    Text Solution

    |

  6. If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is ...

    Text Solution

    |

  7. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

    Text Solution

    |

  8. If x=9 is the chord of contact of tangents of x^(2)-y^(2)=9, then show...

    Text Solution

    |

  9. Show that the equationi of the rectanglar hyperbola whose focus is (1,...

    Text Solution

    |

  10. The hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 has its conjugate axis 5 and p...

    Text Solution

    |

  11. Tangents are drawn from points on the hyperbola x^(2)/9-y^(2)/4=1 to t...

    Text Solution

    |

  12. If a hyperbola passes through a focus of the ellipse and it transverse...

    Text Solution

    |

  13. A hyperbola having the transverse axis of length 2 sin theta, is confo...

    Text Solution

    |

  14. An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1). I...

    Text Solution

    |

  15. The locus represented by x=(a)/(2)(t+(1)/(t)),y=(a)/(2)(t-(1)/(t)) i...

    Text Solution

    |

  16. If the normal at (x(i) y(i)) i=1,2,3,4 on xy=c^2 meet at the point (al...

    Text Solution

    |

  17. Given the base BC of the triangle ABC and if angleC-angleB=k, a consta...

    Text Solution

    |

  18. The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is pr...

    Text Solution

    |

  19. Given the base of the triangle and the sum of tangent of base angles a...

    Text Solution

    |

  20. From a fixed point A(x(1),y(1)) a variable straight line is drawn to c...

    Text Solution

    |