Home
Class 11
MATHS
If the ellipse (x^2)/4+y^2=1 meets the e...

If the ellipse `(x^2)/4+y^2=1` meets the ellipse `x^2+(y^2)/(a^2)=1` at four distinct points and `a=b^2-5b+7,` then `b` does not lie in `[4,5]` (b) `(-oo,2)uu(3,oo)` `(-oo,0)` (d) `[2,3]`

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

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

If a point (a,2) lies between the lines x-y-1=0 and 2(x-y)-5=0 , then the set of values of a is (A) (-oo,3)uu(9/2,oo) (B) (3,9/2) (C) (-oo,3) (D) (9/2,oo)

If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real and distinct, then the value of a in a. (-oo,3] b. (-oo,-2)uu(2,oo) c. [-2,2] d. [-3,oo)

If 3 - 2x^(2) gt 5x, x in R , then the set of solutions is A. (- oo,-1/2) B. (3,oo) C. (-1/2,3) D. [-1/2,3]

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval (-oo,-4) (b) (-oo,0) (4,oo) (d) none of these

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval a) (-oo,-4) (b) (-oo,0) c) (4,oo) (d) none of these

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

If the point (2,k) lies outside the circles x^2+y^2+x-2y-14=0a n dx^2+y^2=13" then k" lies in the interval (a) (-3,-2)uu(3,4) (b) (-3,4) (c) (-oo,-3)uu(4,oo) (d) (-oo-2)uu(3,oo)

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If the vertex of a hyperbola bisects the distance between its center ...

    Text Solution

    |

  2. Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 a...

    Text Solution

    |

  3. If the ellipse (x^2)/4+y^2=1 meets the ellipse x^2+(y^2)/(a^2)=1 at fo...

    Text Solution

    |

  4. The equation 16 x^2-3y^2-32 x+12 y-44=0 represents a hyperbola. (a)the...

    Text Solution

    |

  5. If the base of a triangle and the ratio of tangent of half of base ang...

    Text Solution

    |

  6. S1, S2, are foci of an ellipse of major axis of length 10 units and P ...

    Text Solution

    |

  7. Let L L ' be the latus rectum through the focus of the hyperbola (x^2)...

    Text Solution

    |

  8. Find the equation of the common tangent in the first quadrant of the c...

    Text Solution

    |

  9. If the normal at P(theta) on the hyperbola (x^2)/(a^2)-(y^2)/(2a^2)=1 ...

    Text Solution

    |

  10. The eccentricity of the hyperbola whose length of the latus rectum is ...

    Text Solution

    |

  11. Prove that in an ellipse, the perpendicular from a focus upon any tang...

    Text Solution

    |

  12. Find the asymptotes of the curve xy-3y-2x=0.

    Text Solution

    |

  13. With one focus of the hyperbola x^2/9-y^2/16=1 as the centre, a circle...

    Text Solution

    |

  14. The equation of the passing through the of the ellipse (x^(2))/(16)+(y...

    Text Solution

    |

  15. Two circles are given such that they neither intersect nor touch. Then...

    Text Solution

    |

  16. lf the eccentricity of the hyperbola x^2-y^2(sec)^2alpha=5 is sqrt3 ...

    Text Solution

    |

  17. An ellipse has O B as the semi-minor axis, Fa n dF ' as its foci...

    Text Solution

    |

  18. If A ,B ,a n dC are three points on the hyperbola x y=c^2 such that A ...

    Text Solution

    |

  19. Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0...

    Text Solution

    |

  20. Find the co-ordinates of all the points P on the ellipse, x^2/a^2+y^2/...

    Text Solution

    |