Home
Class 11
MATHS
Two concentric ellipses are such that th...

Two concentric ellipses are such that the foci of one are on the other and their major axes are equal. Let `ea n de '` be their eccentricities. Then. the quadrilateral formed by joining the foci of the two ellipses is a parallelogram the angle `theta` between their axes is given by `theta=cos^(-1)sqrt(1/(e^2)+1/(e^('2))=1/(e^2e^('2)))` If `e^2+e^('2)=1,` then the angle between the axes of the two ellipses is `90^0` none of these

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

Two concentric ellipse be such that the foci of one be on the other and if 3/5 and 4/5 be their eccentricities. If theta is the angle between their axes, then the values of 2(1+sin^(2)theta+sin^(4)theta) must be

If the length of the semi-major axis of an ellipse is 68 and e = 1/2, then the area of the rectangle formed by joining the vertices of latusrecta of the ellipse is equal to

If ea n de ' the eccentricities of a hyperbola and its conjugate, prove that 1/(e^2)+1/(e '^2)=1.

Find the equation of the ellipse whose centre is at origin, the distance between foci is 2 and eccentricity is (1)/(sqrt(2)) .

The eccentricity of an ellipse with centre at the orgin and axes along the coordinate axes , is 1/2 if one of the directrices is x=4, the equation of the ellipse is

Find the equation of the ellipse in the following case: eccentricity e=1/2 and semi major axis =4 .

Find the equation of the ellipse in the following case: eccentricity e=1/2 and major axis =12

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1) , and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e_1a n de_2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that 1/(e1 2)+1/(e2 2)=2 .

Let S, S' be the focil and BB' be the minor axis of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1. If angle BSS' = theta , then the eccentricity e of the ellipse is equal to

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is...

    Text Solution

    |

  2. An ellipse and a hyperbola have their principal axes along the coor...

    Text Solution

    |

  3. Two concentric ellipses are such that the foci of one are on the other...

    Text Solution

    |

  4. If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ell...

    Text Solution

    |

  5. If the tangent drawn at point (t^2,2t) on the parabola y^2=4x is the s...

    Text Solution

    |

  6. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

    Text Solution

    |

  7. Statement 1 : Any chord of the conic x^2+y^2+x y=1 through (0, 0) is b...

    Text Solution

    |

  8. Find the coordinates of the foci, the eocentricity, the latus rectum, ...

    Text Solution

    |

  9. Statement 1 : If there is exactly one point on the line 3x+4y+5sqrt...

    Text Solution

    |

  10. If the latus rectum of a hyperbola forms an equilateral triangle with ...

    Text Solution

    |

  11. Statement 1 : For the ellipse (x^2)/5+(y^2)/3=1 , the product of the p...

    Text Solution

    |

  12. If the latus rectum subtends a right angle at the center of the hyp...

    Text Solution

    |

  13. Statement 1 : The locus of the center of a variable circle touching...

    Text Solution

    |

  14. If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1...

    Text Solution

    |

  15. Statement 1 : A triangle A B C right-angled at A moves so that its per...

    Text Solution

    |

  16. Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-t...

    Text Solution

    |

  17. A ray emanating from the point (5, 0) is INCIDENT on the hyperbola 9x^...

    Text Solution

    |

  18. Statement 1 : If the line x+y=3 is a tangent to an ellipse with focie ...

    Text Solution

    |

  19. Normal is drawn at one of the extremities of the latus rectum of the ...

    Text Solution

    |

  20. Statement 1 : The area of the ellipse 2x^2+3y^2=6 is more than the are...

    Text Solution

    |