Home
Class 12
MATHS
If e and e' be the eccentricities of a h...

If e and e' be the eccentricities of a hyperbolas `xy=c^2 and x^2-y^2=c^2 , ` then `e^2+e'2` equals :

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos
  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos

Similar Questions

Explore conceptually related problems

If e and e' be the eccentricities of a hyperbola and its conjugate , then 1/e^2+1/(e'^2) equals :

If e_1 and e_2 are eccentricities of two hyperbolas : x^2/a^2-y^2/b^2=1 and x^2/b^2-y^2/a^2=1 , then :

If e_(1) and e_(2) are the eccentricities of a hyperbola and its conjugate then

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

If e_(1)ande_(2) are the ecentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate , then

If e_1 and e_2 are the eccentricities of a hyperbola and its conjugate then prove that (1)/(e_1^2)+(1)/(e_2^2)=1 .

If e and e^(prime) are eccentricities of a hyperbola its conjugate, then (1)/(e^(2))+(1)/((e^(1))^(2))=

If e and e^(prime) are the eccentricities of the ellipse 5 x^(2)+9 y^(2)=45 and the hyperbola 5 x^(2)-4 y^(2)=45 respectively, then ee'=

If e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , (altb) then

HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. Equation of the conic with focus at (1,-1) directrix along x-y+1=0 and...

    Text Solution

    |

  2. If e(1) and e(2) are the eccentricities of a hyperbola and its conjuga...

    Text Solution

    |

  3. If e and e' be the eccentricities of a hyperbolas xy=c^2 and x^2-y^2=c...

    Text Solution

    |

  4. The angle between the asymptotes of the hyperbola 3 x^(2)-y^(2)=3 is

    Text Solution

    |

  5. The eccentricity of the hyperbola 9 x^(2)-16 y^(2)+72 x-32 y-16=0 is

    Text Solution

    |

  6. The vertices of a hyperbola are (2,0),(-2,0) and the foci are (3,0),(-...

    Text Solution

    |

  7. The equation of a line which touches both the curves y^(2)=4 x and 3 x...

    Text Solution

    |

  8. The eccentricity of the hyperbola 4 x^(2)-9 y^(2)=2 a x+b^(2) is

    Text Solution

    |

  9. The product of the perpendicular from any poitn P(x,y) on the hyperbol...

    Text Solution

    |

  10. The product of the perpendicular from any poitn P(x,y) on the hyperbol...

    Text Solution

    |

  11. If e and e^(prime) are the eccentricities of the ellipse 5 x^(2)+9 y^(...

    Text Solution

    |

  12. If the eceentricity of a hyperbola is sqrt(7) then the eccentricity of...

    Text Solution

    |

  13. Any point on the hyperbola ((x+1)^(2))/(16)-((y-2)^(2))/(4)=1 is of ...

    Text Solution

    |

  14. The equation of the hyperbola in the standard form (with transverse ax...

    Text Solution

    |

  15. The line x+y=sqrt(2) p will touch the hyperbola 4 x^(2)-9 y^(2)=36, if

    Text Solution

    |

  16. The difference of focal distance of any point on the hyperbola (x^(2))...

    Text Solution

    |

  17. The tangents from a point (2 sqrt(2), 1) to the hyperbola 16 x^(2)-25 ...

    Text Solution

    |

  18. The locus of the point of intersection of perpendicular tangents to th...

    Text Solution

    |

  19. The angle between the two asymptotes of the hyperbola (x^(2))/(16)-(y^...

    Text Solution

    |

  20. The product of the perpendicular from any poitn P(x,y) on the hyperbol...

    Text Solution

    |