Home
Class 12
MATHS
A parabola y=a x^2+b x+c crosses the x-a...

A parabola `y=a x^2+b x+c` crosses the x-axis at `(alpha,0)(beta,0)` both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is: `sqrt((b c)/a)` (b) `a c^2` (d) `sqrt(c/a)`

A

`sqrt((bc)/a)`

B

`ac^2`

C

`b/a`

D

`sqrt(c/a)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|24 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise For Session 2|25 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) both to the right of the origin. A circle also pass through these two points. The length of a tangent from the origin to the circle is sqrt((b c)/a) (b) a c^2 (c) b/a (d) sqrt(c/a)

A parabola y=ax^(2)+bx+c crosses the x- axis at (alpha,0)(beta,0) both to the right of the origin.A circle also passes through these two points.The length of a tangent from the origin to the circle is: sqrt((bc)/(a))( b) ac^(2)(d)sqrt((c)/(a))

A parabola y=ax^(2)+bx+c(ac>0) crosses the x-axis at A and B .A variable circle is drawn passing through A and B .The length of a tangent from the origin to the circle is

Find the equation of the circle passing through the origin and through the points of contact of tangents from the origin to the circle. x^(2) + y^(2) - 11x + 13y + 17 = 0

The locus of the centere of a circle which passes through the point (0,0) and cuts off a length 2b from the line x=c is-

Find the equation to the circle,of radius a , which passes through the two points on the axis of x which are at a distance b from the origin.

Points are A(-2,0), B(0,2), C(2,0) which point lies to the right of the origin on x-axis

ARIHANT MATHS-PARABOLA-Exercise (Single Option Correct Type Questions)
  1. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

    Text Solution

    |

  2. If a!=0 and the line 2bx+3cy+4d=0 passes through the points of interse...

    Text Solution

    |

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

    Text Solution

    |

  4. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

    Text Solution

    |

  5. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  6. If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be...

    Text Solution

    |

  7. Length of the shortest normal chord of the parabola y^2=4ax is

    Text Solution

    |

  8. The largest value of a for which the circle x^2 +y^2 = a^2 falls total...

    Text Solution

    |

  9. From a point (sintheta,costheta), if three normals can be drawn to the...

    Text Solution

    |

  10. If two different tangents of y^2=4x are the normals to x^2=4b y , then

    Text Solution

    |

  11. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |

  12. Normals at two points (x1,x2) and (x2,y2) of the parabola y^2=4x meet ...

    Text Solution

    |

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

    Text Solution

    |

  14. An equilateral triangle SAB in inscribed in the parabola y^2 = 4ax hav...

    Text Solution

    |

  15. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

    Text Solution

    |

  16. Let S be the focus of y^2=4x and a point P be moving on the curve such...

    Text Solution

    |

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

    Text Solution

    |

  18. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  19. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  20. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |