Home
Class 11
MATHS
The equation x^2/(2-lambda)+y^2/(lambda-...

The equation `x^2/(2-lambda)+y^2/(lambda-5)+1=0` represents an ellipse if:

A

rgt2

B

rgt5

C

2lt rlt 5

D

None of these.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

The equation (x^(2))/(10-lambda)+(y^(2))/(6-lambda)=1 represents

The equation (x^(2))/(10-a)+(y^(2))/(4-a)=1 represents an ellipse , if

Given f is increasing, the equation x^(2)/(f(2a))+y^(2)/(f(a^(2)-3))=1 represents an ellipse with X-axis as major axis if

If the equation lambda x^2+(2 lambda-3)y^2-4x-1=0 represents a circle, then its radius is :

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

If x^(2)/(f(4a))+y^(2)/(f(a^(2)-5)) =1 represents an ellipse with major axis as Y-axis and f is a decreasing function,then

Let a,b,c be the sides of a triangle. No two of them are equal and lambda in R If the roots of the equation x^2+2(a+b+c)x+3lambda(ab+bc+ca)=0 are real, then (a) lambda 5/3 (c) lambda in (1/5,5/3) (d) lambda in (4/3,5/3)

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. The eccentricity of the conic 4x^2-9y^2=2 is :

    Text Solution

    |

  2. If e, e’ be the eccentricities of two conics S and S’ and if e^2 + e’^...

    Text Solution

    |

  3. The equation x^2/(2-lambda)+y^2/(lambda-5)+1=0 represents an ellipse i...

    Text Solution

    |

  4. The length of the latus-rectum of the parabola x^2- 4x-8y +12= 0 is:

    Text Solution

    |

  5. The focus of the parabola y = 2x^2 + x is

    Text Solution

    |

  6. The axis of the parabola 9y^2-16x-12y-57=0 is :

    Text Solution

    |

  7. The equation x^(2)+3y^(2)-9x+2y+1=0 represents

    Text Solution

    |

  8. A bridge is in the shape of a semi-ellipse. It is 400 metres One and h...

    Text Solution

    |

  9. The eccentricity of the ellipse4x^2 + 9y^2 = 36 is :

    Text Solution

    |

  10. The foci of the ellipse 9x^2 +4y^2 =36 are

    Text Solution

    |

  11. The foci of the ellipse 25(x+1)^2 + 9(y+2)^2 = 225, are at :

    Text Solution

    |

  12. The lines a(1)x+b(1)y+c(1)=0 and a(2)x+b(2)y+c(2)=0 are perpendicular ...

    Text Solution

    |

  13. The equation of straight line passing through the point (2, 3) and per...

    Text Solution

    |

  14. The equations y=x sqrt3, y =1 are the sides of :

    Text Solution

    |

  15. If a,b,c are in AP then ax + by + c = 0 represents

    Text Solution

    |

  16. The coordinates of the foot of the perpendicular from (2,3) to the lin...

    Text Solution

    |

  17. Find the orthocentre of the triangle formed by the lines xy = 0 and x+...

    Text Solution

    |

  18. If the sum of the distances of a variable point from two perpendicular...

    Text Solution

    |

  19. Point Q is symmetric to P (4, -1) with respect to the bisector of the ...

    Text Solution

    |

  20. The radius of the circle, which is touched by the line y= x and has it...

    Text Solution

    |