Home
Class 11
MATHS
If a hyperbola passes through the foci o...

If `a` hyperbola passes through the foci of the ellipse `(x^2)/(25)+(y^2)/(16)=1` . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of `a.` hyperbola is `(x^2)/9-(y^2)/(16)=1` `b.` the equation of hyperbola is `(x^2)/9-(y^2)/(25)=1` `c.` focus of hyperbola is (5, 0) `d.` focus of hyperbola is `(5sqrt(3),0)`

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 eccentricity of the hyperbola x^2-y^2=4 is

the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 is

The equation of the passing through the of the ellipse (x^(2))/(16)+(y^(2))/(9)=1 , and having centre at (0,3) is :

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

The distance between the foci of a hyperbola is 16 and its eccentricity is sqrt(2) then equation of the hyperbola is

The foci of the hyperbola 4x^2-9y^2=36 is

In each of the find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. (x^(2))/(16)-(y^(2))/(9)=1

The foci of the ellipse x^2/25+y^2/9=1 coincide with a hyperbola. If e=2 for hyperbola, find the equation of hyperbola.

Let the equation of an ellipse be (x^(2))/(144)+(y^(2))/(25)=1 . Then the radius of the circle with centre (0, sqrt(2)) and passing through the foci of the ellipse is

The foci of a hyperbola coincide with the foci of the ellipse x^2/25 +y^2/9 =1 . Find the equation of the hyperbola if its eccentricity is 2.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the equations of tangents to the curve 4x^(2)-9y^(2)=1 which are ...

    Text Solution

    |

  2. Find the value of m for which y=mx+6 is a tangent to the hyperbola (x^...

    Text Solution

    |

  3. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

    Text Solution

    |

  4. One the x-y plane, the eccentricity of an ellipse is fixed (in size a...

    Text Solution

    |

  5. Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1).

    Text Solution

    |

  6. The equation of one directrix of a hyperbola is 2x+y=1, the correspond...

    Text Solution

    |

  7. The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the cent...

    Text Solution

    |

  8. A hyperbola having the transverse axis of length 2sintheta is confocal...

    Text Solution

    |

  9. If it is posssible to draw the tangent to the hyperbola (x^(2))/(a^(2)...

    Text Solution

    |

  10. The set of values of m for which it is possible to draw the chord y=sq...

    Text Solution

    |

  11. Find the equations of the tangents to the hyperbola x^(2)-9y^(2)=9 tha...

    Text Solution

    |

  12. Let a and b be nonzero real numbers. Then the equation (a x^2+b y^2+c)...

    Text Solution

    |

  13. x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will represent ellipse if r lies in the...

    Text Solution

    |

  14. Find the equations to the common tangents to the two hyperbolas (x^2)/...

    Text Solution

    |

  15. Let P(6, 3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)...

    Text Solution

    |

  16. Find the equation of the common tangent to the curves y^2=8x and xy=-1...

    Text Solution

    |

  17. If the maximum distance of any point on the ellipse x^2+2y^2+2x y=1 f...

    Text Solution

    |

  18. An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The ecc...

    Text Solution

    |

  19. The number of points on the ellipse (x^2)/(50)+(y^2)/(20)=1 from which...

    Text Solution

    |

  20. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

    Text Solution

    |