Home
Class 12
MATHS
Let the foci and length of the latus rec...

Let the foci and length of the latus rectum of an ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,a gt b` be `(+-5,0)` and `sqrt(50)` ,respectively.Then,the square of the eccentricity of the hyperbola `(x^(2))/(b^(2))-(y^(2))/(a^(2)b^(2))=1` equals

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

Similar Questions

Explore conceptually related problems

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

If the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=-1 is (5)/(4) , then b^(2) is equal to

Length of latus -rectum of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 is ................. .

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

The locus of extremities of the latus rectum of the family of ellipse b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2) is

If the normal at the end of latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through (0,b) then e^(4)+e^(2) (where e is eccentricity) equals

If the latus rectum of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=1 is (9)/(2) , then its eccentricity, is

Find the equation of the normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the positive end of the latus rectum.

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. Let S=(-1,oo) and f:S rarr R be defined as f(x)=int(-1)^(x)(e^(t)-1)^(...

    Text Solution

    |

  2. If the integral 525int(0)^((pi)/(2))sin2x cos^((11)/(2))x(1+Cos^((5)/(...

    Text Solution

    |

  3. Let the foci and length of the latus rectum of an ellipse (x^(2))/(a^(...

    Text Solution

    |

  4. Let f:R to R be a function defined by f(x)=(4^x)/(4^x+2) and M=int(f(a...

    Text Solution

    |

  5. Let Q and R be the feet of perpendiculars from the point P(a,a,a) on t...

    Text Solution

    |

  6. If F :(- oo, -1] rightarrow (a, b] is defined as f(x) = e^(x^3-3x+1) s...

    Text Solution

    |

  7. The area of the region enclosed by the parabolas y=4x-x^(2) and 3y=(x-...

    Text Solution

    |

  8. Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid,circum...

    Text Solution

    |

  9. Consider the function f:(0,oo)rarr R defined by f(x)=e^(-|log(e)x|) .I...

    Text Solution

    |

  10. Let z(1) and z(2) be two complex numbers such that z(1)+z(2)=5 and z(1...

    Text Solution

    |

  11. If for some m,n,^(6)C(m)+2(""^(6)C(m+1))+^(6)C(m+2)>^(8)C(3) and ^(n-1...

    Text Solution

    |

  12. If a = sin^(-1) (sin 5) and b = cos^(-1) (cos 5) then value of a^2 + b...

    Text Solution

    |

  13. If the mean and variance of 6 observations a, b, 68, 44, 48, 60 are 55...

    Text Solution

    |

  14. Let a variable line passing through the centre of the circle x^(2)+y^(...

    Text Solution

    |

  15. Let 2^("nd"),8^("th") and 44^("th") terms of a non-constant A.P. be re...

    Text Solution

    |

  16. An ellipse frac{x^2}{a^2}+frac{y^2}{b^2}=1 (a> b) whose eccentircity i...

    Text Solution

    |

  17. Let f,g:(0,oo)rarr R be two functions defined by f(x)=int(-x)^(x)(|t|-...

    Text Solution

    |

  18. Let f:rarr R rarr(0,oo) be strictly increasing function such that lim(...

    Text Solution

    |

  19. The temperature T(t) of a body at time t=0 is 160^(@)F and it decrease...

    Text Solution

    |

  20. The shortest distance,between lines L(1) and L(2) ,where L(1):(x-1)/(2...

    Text Solution

    |