Home
Class 12
MATHS
If (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is ...

If `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is an ellipse and tangent at any point cuts the co-ordinate axes at P and Q, then the minimum area of triangle OPQ is :

A

ab

B

`(a^(3)+b^(3)+a b)/(3)`

C

`a^(2)+h^(2)`

D

`(a^(2)+b^(2))/(4)`

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

The tangent to the curve xy = 25 at any point on it cuts the coordinate axes at A and B , then the area of the triangle OAB is

The line x+y -2 =0 cuts the axes at A and B , then the incentre of triangle AOB is

The plane x/4 + y/3 -z/5 =1 cuts the axes at A, B, C then the area of the triangle ABC is

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 :

The plane x/2+y/3+z/4 = 1 cuts the axes A, B, C then the area of the triangle ABC 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

If S_(1) and S_(2) are the foci of (x^(2))/(25)+(y^(2))/(16)=1 and P is any point on it, then the maximum area of the triangle P S_(1) S_(2) is

If S_(1) and S_(2) are the foci of (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and P is any point on it, then the area P S_(1) S_(2) will be maximum, when P =

If a normal at any point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) meet the major and minor axes at M and N respectively, such that (P M)/(P N)=(2)/(3) , then the eccentricity =

An ellipse is drawn by taking the diameter of the circle (x-1)^(2)+y^(2)=1 as semi-minor axis and a diameter of the circle x^(2)+(y-2)^(2)=4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the co-ordinate axes, then the equation of the ellipse is :

HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
  1. Let E be the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and C be the circle x^(...

    Text Solution

    |

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

    Text Solution

    |

  3. If (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is an ellipse and tangent at any ...

    Text Solution

    |

  4. Let P(x(1), y(1)) and Q(x(2), y(2)), y(1) lt 0, y(2) lt 0 be the end p...

    Text Solution

    |

  5. The normal at a point P on the ellipse x^(2)+4y^(2)=16 meets the x-axi...

    Text Solution

    |

  6. The line passing through the extremity A of the major axis and extremi...

    Text Solution

    |

  7. A focus of an ellipse is at the origin. The directrix is the line x=4 ...

    Text Solution

    |

  8. The ellipse x^(2)+4 y^(2)=4 is inscribed in a rectangle aligned with c...

    Text Solution

    |

  9. Equation of the ellipse whose axes are the axes of co-ordinates and wh...

    Text Solution

    |

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

    Text Solution

    |

  11. The eccentricity of the ellipse 9 x^(2)+5 y^(2)-30 y=0 is

    Text Solution

    |

  12. The eccentricity of an ellipse with centre at the origin which meets t...

    Text Solution

    |

  13. The equation to the ellipse (referred to its axes as the axes of x and...

    Text Solution

    |

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

    Text Solution

    |

  15. The line L x+m y+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2)...

    Text Solution

    |

  16. The angle between the pair of tangents drawn from the point (1,2) to t...

    Text Solution

    |

  17. How many real tangents can be drawn to the ellipse 5 x^(2)+9 y^(2)=32 ...

    Text Solution

    |

  18. If two tangents drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1...

    Text Solution

    |

  19. The foci of the conic 25 x^(2)+16 y^(2)-150 x=175 are

    Text Solution

    |

  20. The equation of the ellipse whose distance between the foci is equal t...

    Text Solution

    |