Home
Class 12
MATHS
Consider an ellipse E:x^(2)/a^(2)+y^(2)/...

Consider an ellipse E:`x^(2)/a^(2)+y^(2)/b^(2)=1`, centered at point 'O' and having AB and CD as its major and minor axes respectively if `S_1`be one of the focus of the ellipse, radius of the incircle of `DeltaOCS_1 ` be 1 unit and `OS_1=6` units.
Q. if the ellipse (E) is ∆sq unit, then the value of 4`Delta` is

A

`63pi`

B

`64pi`

C

`65pi`

D

`66pi`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise For Session 2|15 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

Similar Questions

Explore conceptually related problems

Consider an ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centered at point O andhaving AB and CD as its major and minor axes,respectively.If S_(1) is one of the focus of the ellipse,the radius of the incircle of triangle OCS_(1) is unit,and OS_(1)=6 units, then the value of (a-b)/(2) is

An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of the foci of the ellipse, the radius of the incircle of triangle OCS_(1) be 1 unit, and OS_(1)=6 units The perimeter of DeltaOCS_(1) is

F is one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with O as centre. bar(AB) and bar(CD) are major and minor axes respectively. If OF=6 and the diameter of the incircle of triangle OCF is 2. The values of a & b are

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 with the major and minor axis in M and m respectively is

A tangent having slope of -(4)/(3) to the ellipse (x^(2))/(18)+(y^(2))/(32)=1 intersects the major and minor axes at points A and B, respectively.If C is the center of the ellipse,then find area of triangle ABC.

S and T are the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and B is an end of the minor axis.If STB is an equilateral triangle,the eccentricity of the ellipse is e then find value of 4e

point 'O' is the centre of the ellipse with major axis AB & miror axis CD. Point F is one focus of the ellipse. If OF=6 & the diameter of the inscrided circle of triangle OCF is 2, then the products (AB) (CD) is

If the distance between the parallel tangents to the ellipse (x^(2))/(4)+(y^(2))/(1)=1 is 3 units then the slope is

ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider an ellipse E:x^(2)/a^(2)+y^(2)/b^(2)=1, centered at point 'O'...

    Text Solution

    |

  2. The muinimum area of the triangle formed by the tangent to (x^(2))/(a...

    Text Solution

    |

  3. Find the equation of the common tangent in the 1st quadrant to the cir...

    Text Solution

    |

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

    Text Solution

    |

  5. In an ellipse, the distances between its foci is 6 and minor axis is 8...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

  9. The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at...

    Text Solution

    |

  10. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  11. The conic having parametric representation x=sqrt3((1-t^(2)/(1+t^(2)))...

    Text Solution

    |

  12. The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with...

    Text Solution

    |

  13. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

    Text Solution

    |

  14. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

    Text Solution

    |

  15. Tangents are drawn from the point P(3,4) to the ellipse (x^2)/(9)+(y^2...

    Text Solution

    |

  16. Equation of the ellipse whose axes are the axes of coordinates and ...

    Text Solution

    |

  17. The ellipse E1:(x^2)/9+(y^2)/4=1 is inscribed in a rectangle R whose s...

    Text Solution

    |

  18. Statement 1: An equation of a common tangent to the parabola y^2=16...

    Text Solution

    |

  19. An ellipse is drawn by taking a diameter of the circle (x""""1)^2+""y^...

    Text Solution

    |

  20. the equation of the circle passing through the foci of the ellip...

    Text Solution

    |

  21. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |