Home
Class 12
MATHS
If (a, 0) is a point on a diameter of th...

If (a, 0) is a point on a diameter of the circle `x^(2)+y^(2)=4`, then the equation `x^(2)-4x-a^(2)=0` has

A

Exactly one real root in `[-1,0]`

B

Exactly one real root in `[2,5]`

C

Distinct roots greater than `-1`

D

Distinct roots less than 5

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

If (1,2) (2,a) are extremities of a diameter of the circle x^(2)+y^(2)_3x-4y+6=0 then a=

The length of the diameter of the circle x^2+y^2−4x−6y+4=0

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

Equation of a common tangent to the circle x^(2)+y^(2)-6x=0 and the parabola y^(2)=4x is

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

A foot of the normal from the point (4, 3) to a circle is (2, 1) and a diameter of the circle has the equation 2x -y -2 =0 . Then the equation of the circle is:

If one end of a diameter of the circle x^(2) + y^(2) - 4x - 6y + 11 = 0 is (3, 4), then the coordinates of the other end of the diameter are

If (4, 1) be an end of a diameter of the circle x^2 + y^2 - 2x + 6y-15=0 , find the coordinates of the other end of the diameter.

The length of the tangent from a point on the circle x^(2)+y^(2)+4x-6y-12=0 to the circle x^(2)+y^(2)+4x-6y+4=0 is

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. The expression (1)/(sqrt(x+2sqrt(x-1)))+(1)/(sqrt(x-2sqrt(x-1))) simp...

    Text Solution

    |

  2. if allvalues of x which satisfies the inequality log ((1//3))(x ^(2) +...

    Text Solution

    |

  3. If (a, 0) is a point on a diameter of the circle x^(2)+y^(2)=4, then t...

    Text Solution

    |

  4. Let x^2-px+q=0, where p in R,q in R have the roots alpha,beta such tha...

    Text Solution

    |

  5. If a, b, c are positive numbers such that a gt b gt c and the equation...

    Text Solution

    |

  6. For the quadratic polynomial f (x) =4x ^(2)-8ax+a. the statements (s) ...

    Text Solution

    |

  7. Given a,b, c are three distinct real numbers satisfying the inequality...

    Text Solution

    |

  8. Let f (x) =x ^(2) -4x +c AA x in R, where c is a real constant, then w...

    Text Solution

    |

  9. If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 +...

    Text Solution

    |

  10. If x satisfies |x-1| + |x-2|+|x-3|gt6, then : i)x ∈ (−∞,1) ii)x ∈...

    Text Solution

    |

  11. If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real ...

    Text Solution

    |

  12. If a,b are two numbers such that a ^(2) +b^(2) =7 and a ^(3) + b^(3) =...

    Text Solution

    |

  13. The number of non-negative integral ordered pair(s) (x,y) for which (x...

    Text Solution

    |

  14. If alpha, beta, gamma and delta are the roots of the equation x ^(4) -...

    Text Solution

    |

  15. The value of 'k' for which roots of the equation 4x^2-2x+k=0 are comp...

    Text Solution

    |

  16. If a,b,c in R, then for which of the following graphs of the quadrati...

    Text Solution

    |

  17. If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real ro...

    Text Solution

    |

  18. If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b...

    Text Solution

    |

  19. The equation cos ^(2) x - sin x+lamda = 0, x in (0, pi//2) has roots t...

    Text Solution

    |

  20. If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solutio...

    Text Solution

    |