Home
Class 12
MATHS
Given the base of the triangle and the s...

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.

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

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

The base of a triangle is 80 and one of the base angles is 60^@ . IF the sum of the lengths of the other two sides is 90, then the shortest side is

Classify the following triangles based on the measure of angles.

The sum of the angles in a triangle is equal to two Right angles.

The base of an equilateral triangle is along the line given by 3x+4y=9 . If a vertex of the triangle is (1,2) then length of a side of the triangle is

The ends of the hypotenuse of a right angled triangle are (2,0,-3) ,(0,4,1) then the locus of the third vertex is

The ends of hypotenuse of a right angled triangle are (2, 0, -3), (0,4,1) then locus of third vertex is

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

    |