Home
Class 12
MATHS
Let P be a variable point on the ellipse...

Let P be a variable point on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` with foci `S_(1)andS_(2)`. If A be the area of the triangle `PS_(1)S_(2)`, then the maximum value of A is :

A

`2 a b e`

B

`a b e`

C

none of these

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|390 Videos

  • HYPERBOLA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|162 Videos

Similar Questions

Explore conceptually related problems

Find the area of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1

Equation of the ellipse is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S_(1) and S_(2) The maximum area of the triangle P S_(1) S_(2) , where P is any point on the ellipse is

Let P be a variable point on the ellipse x^(2)/25 + y^(2)/16 = 1 with foci at S and S'. If A be the area of triangle PSS' then the maximum value of A, is

If P is point on (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with focii S and S' then the maximum value of triangle SPS' is

Find the area of the ellipse (x^(2))/(a^(2))+ (y^(2))/(b^(2))=1 by the method of integration.

Area of the ellipse x^(2)/9+y^(2)/4=1 is

The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

The distance of the point theta^(prime) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 from a focus is

If sqrt(3) b x+a y=2 a b is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the eccentric angle of the point is

The foci of the ellipse 25(x+1)^(2)+9(y+2)^(2)=225 are at

HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
  1. The auxilary circle of the ellipse 9 x^(2)+4 y^(2)=1 is

    Text Solution

    |

  2. P is any point on the ellipse 9x^(2) + 36y^(2) = 324 whose foci are S ...

    Text Solution

    |

  3. Let P be a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |

  4. Eccentric angle of a point on the ellipse x^(2)+3 y^(2)=6 at a distanc...

    Text Solution

    |

  5. The eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose...

    Text Solution

    |

  6. The distance of the point theta^(prime) on the ellipse (x^(2))/(a^(2)...

    Text Solution

    |

  7. The number of real tangents that can be drawn to the ellipse 3 x^(2)+5...

    Text Solution

    |

  8. The number of tangents from (4,7) to the ellipse (x^(2))/(16)+(y^(2))/...

    Text Solution

    |

  9. S(1) and S(2) are the foci of an ellipse and B is the end of the minor...

    Text Solution

    |

  10. The length of the latus - rectum of the ellipse (x^(2))/(25) + (y^(2))...

    Text Solution

    |

  11. The length of the major axis is three times the length of minor axis, ...

    Text Solution

    |

  12. An ellipse has OB as a semi-minor axis. S(1),S(2) are its foci and the...

    Text Solution

    |

  13. The equation of the locus of the middle point of the portion of the ta...

    Text Solution

    |

  14. If sqrt(3) b x+a y=2 a b is a tangent to the ellipse (x^(2))/(a^(2))+(...

    Text Solution

    |

  15. If a normal at any point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)...

    Text Solution

    |

  16. Locus of the point of intersection of the tangent at the ends of focal...

    Text Solution

    |

  17. The equation of a common tangent to the circle x^(2)+y^(2)=16 and the ...

    Text Solution

    |

  18. . If P Q andP R are the tangents from P to the ellipse (x^(2))/(2)+y^(...

    Text Solution

    |

  19. If the tangents drawn from a point (1,2 sqrt(3)) to the ellipse (x^(2)...

    Text Solution

    |

  20. Circles are described on the major axis and on the line joining the fo...

    Text Solution

    |