Home
Class 12
MATHS
The radius of the circle passing through...

The radius of the circle passing through the foci of the ellipse `9x^(2) + 16y^(2) = 144` and having its centre at (0, 3), is

A

4

B

3

C

`sqrt(12)`

D

`7//2`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `x^(2)/16 + y^(2)/9 = 1`
The eccentricity e of the ellipse is given by
`e = sqrt(1 - 9/16) = sqrt7/4`
So, the coordinates of the foci are `(pm sqrt7, 0).`
`therefore` Radius of the circle `= sqrt((sqrt7 - 0)^(2) + (0 - 3)^(2)) = 4.`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

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

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Exercise|82 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

Similar Questions

Explore conceptually related problems

The radius of the circle passing through the foci of the ellipse (x^(2))/(16)+(y^(2))/(9) and having its center (0,3) is 4(b)3(c)sqrt(12) (d) (7)/(2)

the equilibrium of the circle passing through the foci of the ellipse (x^(2))/(16)+(y^(2))/(9)=1 and having centre at (0,3) is

The equation of the circle passing through the foci of the ellipse (x^2)/(16)+(y^2)/9=1 , and having centre at (0, 3) is (1) x^2+y^2-6y+7=0 (2) x^2+y^2-6y-5=0 (3) x^2+y^2-6y+5=0 (4) x^2+y^2-6y-7=0

The radius of the circle passing through the foci of (x^(2))/(16) + (y^(2))/(9) =1 , and having centre (0, 3) is

Find the ecentricity and foci of the ellipse 4x^(2) + 9y^(2) = 144

OBJECTIVE RD SHARMA-ELLIPSE-Section I - Solved Mcqs
  1. Ellipses which are drawn with the same two perpendicular lines as axes...

    Text Solution

    |

  2. The eccentricity of the ellipse with centre at the origin which meets ...

    Text Solution

    |

  3. The radius of the circle passing through the foci of the ellipse 9x^(2...

    Text Solution

    |

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

    Text Solution

    |

  5. The focus of an ellipse is (-1, -1) and the corresponding directrix is...

    Text Solution

    |

  6. The equation of the ellipse with its centre at (1, 2), one focus at (6...

    Text Solution

    |

  7. Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), a...

    Text Solution

    |

  8. The area (in sq. units) of the quadrilateral formed by the tangents...

    Text Solution

    |

  9. If alpha-beta= constant, then the locus of the point of intersection o...

    Text Solution

    |

  10. Let S=(3,4) and S'=(9,12) be two foci of an ellipse. If the coordinate...

    Text Solution

    |

  11. Let Sa n dS ' be two foci of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 . I...

    Text Solution

    |

  12. The locus of the foot of the perpendicular from the foci an any tangen...

    Text Solution

    |

  13. The locus of the point of intersection of tangents to the ellipse x^(2...

    Text Solution

    |

  14. The locus of the point of intersection of tangents to the ellipse x^(2...

    Text Solution

    |

  15. Find the locus of the foot of the perpendicular drawn from the cent...

    Text Solution

    |

  16. Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the...

    Text Solution

    |

  17. The locus of the point of intersection of perpendicular tangents to x^...

    Text Solution

    |

  18. Let S=(3,4) and S'=(9,12) be two foci of an ellipse. If the coordinate...

    Text Solution

    |

  19. The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(...

    Text Solution

    |

  20. Let d1a n dd2 be the length of the perpendiculars drawn from the foci ...

    Text Solution

    |