Home
Class 11
MATHS
Radius of the largest circle which passe...

Radius of the largest circle which passes through the focus of the parabola `y^2=4x` and contained in it, is

A

8

B

4

C

2

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
Let r be the radius of the largest circle passi9ng through the focus (1, 0) of `y^(2)=4x.`
Clearly, centre of the circle will be on x-axis and its co-ordinates are n (1+r,0). The equation of the circle id
`(x-1-r)^(2)+y^(2)=r^(2)`

It touches `y^(2)=4x.` Therefore, the equation
`(x-r-1)^(2)+4x=r^(2)` must have equal roots.
`rArr" "4(1-r)^(2)-4(2r+1)=0rArrr=4`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise SECTION-I (SOLVED MCQs EXAMPLE)|1 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

Find the radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and is also contained in it.

The focus of the parabola y^2=x+4y+3 , is :

The focus of the parabola y^(2)-4y-8x-4=0 is

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The focus of the parabola y^(2)-4y-8x+4=0 is,

The focus of the parabola y = 2x^(2) + x is

The focus of the parabola y^(2)-x-2y+2=0 is

The coordinates of the focus of the parabola x^(2)-4x-8y-4=0

Find the coordinates of the vertex and the focus of the parabola y^(2)=4(x+y) .

If the line passing through the focus S of the parabola y=a x^2+b x+c meets the parabola at Pa n dQ and if S P=4 and S Q=6 , then find the value of adot

OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
  1. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

    Text Solution

    |

  2. If normals at the ends of the double ordinate x = 4 of parabola y^(2)=...

    Text Solution

    |

  3. Radius of the largest circle which passes through the focus of the par...

    Text Solution

    |

  4. If the tangents and normals at the extremities of a focal chord of a ...

    Text Solution

    |

  5. The axis of a parabola is along the line y = x and its vertex and focu...

    Text Solution

    |

  6. If the normals from any point on the parabola x^2=4y cut the line y = ...

    Text Solution

    |

  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  8. Minimum distance between the parabola y^2-4x-8y+40=0" and "x^2-8x-4y+4...

    Text Solution

    |

  9. ABCD is a square with side AB = 2. A point P moves such that its dista...

    Text Solution

    |

  10. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  11. If P(1,2sqrt(2)),R(9,0), S(-1,0), then radius of the circumcircle of D...

    Text Solution

    |

  12. In exampla 27, the radius of the incircle of DeltaPQR, is

    Text Solution

    |

  13. Circle described on the focal chord as diameter touches

    Text Solution

    |

  14. If a normal chord subtends a right at the vertex of the parabola y^(2)...

    Text Solution

    |

  15. If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x,...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. If (h ,k) is a point on the axis of the parabola 2(x-1)^2+2(y-1)^2=(x+...

    Text Solution

    |

  18. The radius of the circle whose centre is (-4,0) and which cuts the par...

    Text Solution

    |

  19. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |