Home
Class 11
MATHS
If e1 and e2 are the eccentricities of a...

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`.

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 5

    OSWAAL PUBLICATION|Exercise EXERCISE|52 Videos
  • SAMPLE PAPER 7

    OSWAAL PUBLICATION|Exercise EXERCISE|57 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)ande_(2) are the ecentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate , then

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

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 :

If e_(1) is the eccentricity of the ellipse (x^(2))/(16)+(y^(2))/(25)=1 and e_(2) is the eccentricity of the hyperbola passing through the foci of the ellipse and e_(1) . e_(2)=1 , then the equation of the hyperbola

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 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) and e_(2) are eccentricities of the ellipse (x^(2))/(18)+(y^(2))/(4)=1 and the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 respectively, then the relation between e_(1) and e_(2) is

int(e^(2x) -1)/(e^(2x) + 1) dx

f(x) = ((e^(2x)-1)/(e^(2x)+1)) is

OSWAAL PUBLICATION-SAMPLE PAPER 6-EXERCISE
  1. Let f={(1,1), (2,3), (3,5), (4,7)} be a function from Z into Z defined...

    Text Solution

    |

  2. By giving a conter example , show that the statement " For any r...

    Text Solution

    |

  3. If e1 and e2 are the eccentricities of a hyperbola and its conjugate t...

    Text Solution

    |

  4. The sum of first three terms of a G.P is 39//10 and their product is 1...

    Text Solution

    |

  5. find general solution sin x + sin 3x + sin 5x =0

    Text Solution

    |

  6. In how many of distinct permutations of the letters in the word MISSIS...

    Text Solution

    |

  7. (iii) Find the modulus and argument of the complex numbers. (a) (1+i...

    Text Solution

    |

  8. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

    Text Solution

    |

  9. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

    Text Solution

    |

  10. A and B are two events such that P(A) =0.54,P(B) =0.69 and P( A nnB) ...

    Text Solution

    |

  11. Find the derivative of function cot x with respect to x from first pri...

    Text Solution

    |

  12. If a,b,c are in G.P and a^((1)/(x))=b^((1)/(y))=c^((1)/(z)), prove tha...

    Text Solution

    |

  13. Define rational function.If function from f:R-{0} rarr R is defined as...

    Text Solution

    |

  14. Calculate the mean deviation about median for the following distributi...

    Text Solution

    |

  15. cos^(2)A+cos^(2)B-cos^(2)C=1-2sinA sinB cosC

    Text Solution

    |

  16. An examination paper consists of 12 questions diyided in to part A and...

    Text Solution

    |

  17. An examination paper consists of 12 questions diyided in to part A and...

    Text Solution

    |

  18. 1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

    Text Solution

    |

  19. The second ,third and fourth terms in the binomial expansion (x+a)^n a...

    Text Solution

    |

  20. Derive an expression for the distance between two parallel lines y=mx+...

    Text Solution

    |