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)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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 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)

If a hyperbola passes through foci of the ellipse x^2/5^2 + y^2/3^2 = 1 and its transverse and conjugate axes coincide with the major and minor axes of the ellipse and the product of their eccentricities is 1, then the product of length of semi transverse and conjugate axes of hyperbola is...

What are the foci of the hyperbola x^(2)/(36)-y^(2)/(16)=1

Find the eccentricity of hyperbola x^(2)-9y^(2)=1 .

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

The eccentricity of the hyperbola x^(2)-y^(2)=9 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

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Equation of ellipse is : (A) x^2/16 + y^2/9 =1 (B) x^2/25 + y^2/9 = 1 (C) x^2/25 + y^2/16 = 1 (D) none of these

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Foci of the ellipse are (A) (+- 4, 0) (B) (+-3, 0) (C) (+-5, 0) (D) none of these

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

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

    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. Statement 1 : A bullet is fired and it hits a target. An observer i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

    Text Solution

    |

  13. Find the equations of the tangents to the hyperbola x^2-9y^2=9 that ar...

    Text Solution

    |

  14. Let aa n db be nonzero real numbers. Then the equation (a x^2+b y^2+c)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. A parabola is drawn with focus at one of the foci of the ellipse (x^2)...

    Text Solution

    |

  18. Let P(6,3) be a point on the hyperbola x^2/a^2-y^2/b^2=1If the normal ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |