Home
Class 11
MATHS
Find the eccentricity of the hyperbola g...

Find the eccentricity of the hyperbola given by equations `x=(e^t+e^(-t))/2` and `y=(e^t-e^(-t))/3,t in R`.

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

Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-1))/2a n dy=(e^t-e^(-1))/3,t in Rdot

Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

The eccentricity of the conic x=3((1-t^(2))/(1+t^(2))) and y=(2t)/(1+t^(2)) is

A curve is represented parametrically by the equations x=t+e^(at) and y=-t+e^(at) when t in R and a > 0. If the curve touches the axis of x at the point A, then the coordinates of the point A are

The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a hyperbola of eccentricity

In the equation N_(t)=N_(0)e^(rt),'e' is

Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

The eccentricity of the hyperbola x=a/2(t+1/t), y=a/2(t-1/t) is a. sqrt(2) . b. sqrt(3) c. 2sqrt(3) d. 3sqrt(2)

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. An ellipse and a hyperbola are confocal (have the same focus) and the ...

    Text Solution

    |

  9. The point of intersection of the tangents at the point P on the ellips...

    Text Solution

    |

  10. The distance between two directrices of a rectangular hyperbola is 10 ...

    Text Solution

    |

  11. Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2= at th...

    Text Solution

    |

  12. Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1...

    Text Solution

    |

  13. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  14. Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1...

    Text Solution

    |

  15. A circle has the same center as an ellipse and passes through the foci...

    Text Solution

    |

  16. C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangen...

    Text Solution

    |

  17. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

    Text Solution

    |

  18. The angle subtended by common tangents of two ellipses 4(x-4)^2+25 y^2...

    Text Solution

    |

  19. P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/...

    Text Solution

    |

  20. If P Q R is an equilateral triangle inscribed in the auxiliary circle ...

    Text Solution

    |