Home
Class 12
MATHS
Set of value of alpha for which the poin...

Set of value of `alpha` for which the point `(alpha,1)` lies inside the circle `x^(2)+y^(2)-4=0` and parabola `y^(2)=4x` is

A

`|alpha|ltsqrt(3)`

B

`|alpha|lt2`

C

`(1)/(4)ltalphaltsqrt(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(3) We must have
`alpha^(2)+1-4lt0and1-4alphalt0`
`rArralpha^(2)lt3andalphagt(1)/(4)`
`rArr-sqrt(3)ltalphaltsqrt(3)andalphagt(1)/(4)`
`rArr(1)/(4)ltalphaltsqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise (Multiple)|26 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Comprehension)|41 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

The set of values of alpha for which the point (alpha,1) lies ies inside the curves c_(1):x^(2)+y^(2)-4=0 and c_(2):y^(2)=4x is | alpha|

The point (1,2) lies inside the circle x^(2)+y^(2)-2x+6y+1=0 .

Find the value of alpha for which the point (alpha -1, alpha) lies inside the parabola y^(2) = 4x .

The set of values of 'a' for which the point (a-1, a+1) lies outside the circle x^(2)+y^(2)=8 and inside the circle x^(2)+y^(2)-12x+12y-62=0 , is

Find the values of alpha for which the point (alpha-1,alpha+1) lies in the larger segment of the circle x^(2)+y^(2)-x-y-6=0 made by the chord whose equation is x+y-2=0

The range of 'alpha' for which the point (alpha, alpha) lies in minor arc bounded by the curves x^(2)+y^(2)=1 and x+y=1 is

Statement 1: The value of alpha for which the point (alpha,alpha^(2)) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1) .Statement 2: The parabola y=x^(2) meets the linex +y=2 at (0,1) .

The point (2, 4) lies inside the circle x^(2) + y^(2) = 16 . The above statement is

If (alpha,alpha) lies inside the circle x^(2)+y^(2)=9 then find the region of (alpha,alpha)

CENGAGE-PARABOLA-Exercise (Single)
  1. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

    Text Solution

    |

  2. AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is dr...

    Text Solution

    |

  3. Set of value of alpha for which the point (alpha,1) lies inside the ci...

    Text Solution

    |

  4. If X is the foot of the directrix on axis of the parabola. PP' is a d...

    Text Solution

    |

  5. A water jet from a function reaches it maximum height of 4 m at a d...

    Text Solution

    |

  6. Area of the triangle formed by the vertex, focus and one end of latusr...

    Text Solution

    |

  7. The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [...

    Text Solution

    |

  8. Two parabola have the same focus. If their directrices are the x-axis ...

    Text Solution

    |

  9. The locus of the point (sqrt(3h),sqrt(sqrt(3)k+2)) if it lies on the l...

    Text Solution

    |

  10. A circle touches the x-axis and also touches the circle with center (...

    Text Solution

    |

  11. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

    Text Solution

    |

  12. The length of the latus rectum of the parabola whose focus is ((u^2)/(...

    Text Solution

    |

  13. The graph of the curve x^2+y^2-2x y-8x-8y+32=0 falls wholly in the fir...

    Text Solution

    |

  14. The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^...

    Text Solution

    |

  15. If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then ...

    Text Solution

    |

  16. A line is drawn from A(-2,0) to intersect the curve y^2 = 4x in P and ...

    Text Solution

    |

  17. The length of the chord of the parabola y^2=x which is bisected at the...

    Text Solution

    |

  18. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then th...

    Text Solution

    |

  19. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

    Text Solution

    |

  20. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both ...

    Text Solution

    |