Home
Class 11
MATHS
If the distance between the foci of a hy...

If the distance between the foci of a hyperbola is `16` and its eccentricity is `sqrt(2)` , then obtain its equation.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)-y^(2)=32`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(D) (Long Answer Type Questions ) (6 Marks)|21 Videos
  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(B) (Very Short Answer Type) (2 Mark)|8 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Short Answer Type Questions|49 Videos
  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise SHORT ANSWER TYPE QUESTIONS|20 Videos

Similar Questions

Explore conceptually related problems

The distance between foci of a hyperbola is 16 and its eccentricity is sqrt2 , then the equation of hyperbola is

The distance between the foci of a hyperbola is 16 and its eccentricity is sqrt(2) then equation of the hyperbola is x^(2)+y^(2)=32b.x^(2)-y^(2)=16c*x^(2)+y^(2)=16dx^(2)-y^(2)=32

Find the standard equation of hyperbola in each of the following cases: (i) Distance between the foci of hyperbola is 16 and its eccentricity is sqrt2. (ii) Vertices of hyperbola are (pm4,0) and foci of hyperbola are (pm6,0) . (iii) Foci of hyperbola are (0,pmsqrt(10)) and it passes through the point (2,3). (iv) Distance of one of the vertices of hyperbola from the foci are 3 and 1.

If the distance between the foci of a hyperbola with x-axis as the major axis is 16 units and its eccentricity is (4)/(3) , then its equation is

If distance between foci of an ellipse equals its latus-rectrum , then its eccentricity is

Statement- 1 : If the foci of a hyperbola are at (4,1) and (-6,1) and eccentricity is (5)/(4) , then the length of its transverse axis is 4 . Statement- 2 : Distance between the foci of a hyperbola is equal to the product of its eccentricity and length of the transverse axis.

If length of the transverse axis of a hyperbola is 8 and its eccentricity is sqrt(5)//2 then the length of a latus rectum of the hyperbola is

If the distance between the foci of an ellipse is equal to length of minor axis, then its eccentricity is

CBSE COMPLEMENTARY MATERIAL-COORDINATE GEOMETRY-section(C) (Short Answer Type Question) (4 Marks)
  1. Find equation of an ellipse having vetices (0, pm5) and foc (0,pm4).

    Text Solution

    |

  2. If the distance between the foci of a hyperbola is 16 and its eccen...

    Text Solution

    |

  3. Find the equation for the ellipse that satisfies the given conditio...

    Text Solution

    |

  4. If one end of a diameter of the circle x^(2)+y^(2)-4x-6y+11=0 is (3, ...

    Text Solution

    |

  5. Find the equation of the ellipse with foci at (+-5,0)a n dx=(36)/5 as ...

    Text Solution

    |

  6. The foci of a hyperbola coincide with the foci of the ellipse (x^2)...

    Text Solution

    |

  7. Find the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 which passe...

    Text Solution

    |

  8. If the latursrectum of an ellipse is equal to half of its minor-axis, ...

    Text Solution

    |

  9. find equation of circle concentric with circle 4x^2+4y^2-12x-16y-21=0 ...

    Text Solution

    |

  10. Find the equation of a circle whose centre is at (4, -2) and 3x-4y+5=0...

    Text Solution

    |

  11. If equation of the circle is in the form of x^2+y^2+2gx+2fy+c=0 then p...

    Text Solution

    |

  12. The equation (x-x1)(x-x2)+(y-y1)(y-y2=0 Represents a circle whose cent...

    Text Solution

    |

  13. The equation of the circle touching the lines x = 0, y=0 and x= 2c is-

    Text Solution

    |

  14. Find the equation of the parabola having focus at (-1,-2) and directri...

    Text Solution

    |

  15. Find the equation of the set of all points the sum of whose distanc...

    Text Solution

    |

  16. Show that the set all points such that the difference of their dist...

    Text Solution

    |

  17. if OXPY is a square of side 4 cm in first quadrant, where O is the ori...

    Text Solution

    |