Home
Class 12
MATHS
The tangent at a point P(acosvarphi,bsin...

The tangent at a point `P(acosvarphi,bsinvarphi)` of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

A

`(1 + sin^2 theta)^(-1)`

B

`(1 + sin^2 theta)^(-1//2)`

C

`(1 + sin^2 theta)^(-3//2)`

D

`(1 + sin^2 theta)^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (2) (True and False)|4 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (2) (Fill in the blanks)|6 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (1) (Fill in the blanks)|4 Videos

  • THE CIRCLE

    ML KHANNA|Exercise Self Assessment Test (Fill in the blanks) |7 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise SELF ASSESSMENT TEST |4 Videos

Similar Questions

Explore conceptually related problems

The tangent at a point P(a cos phi,b sin phi) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets its auxiliary circle at two points,the chord joining which subtends a right angle at the center.Find the eccentricity of the ellipse.

If the tangent at theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxiliary circle at two points which subtend a right angle at the centre then e^(2)(2-cos^(2)theta) =

The tangent at the point alpha on the ellipse x^2/a^2+y^2/b^2=1 meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity 'e' of the ellipse is given by the equation (A) e^2(1+cos^2alpha)=1 (B) e^2(cosec^2alpha-1)=1 (C) e^2(1+sin^2alpha)=1 (D) e^2(1+tan^2alpha)=1

If the tangent at theta on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 meets the auxiliary circle at two points which subtend a right angle at the centre,then e^(2)(2-cos^(2)theta)=

The tangent at the point alpha on a standard ellipse meets the auxiliary circle in two points which subtends a right angle at the centre. Show that the eccentricity of the ellipse is (1+ sin^2aplha)^-1/2 .

If the chord joining the points (2,-1),(1,-2) subtends a right angle at the centre of the circle,then its centre and radius are

" Eccentricity of ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 " such that the line joining the foci subtends a right angle only at two points on ellipse is "

At some point P on the ellipse the segments ss' subtends a right angle then its eccentricity

Locus of the middle points of chords of the circle x^(2)+y^(2)=16 which subtend a right angle at the centre is

ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
  1. Tangents are drawn to x^2 + 3y^2 = 2. The locus" of mid-point of inter...

    Text Solution

    |

  2. Tangents are drawn to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 at points ...

    Text Solution

    |

  3. The locus of the point of intersection of tangents to an ellipse at tw...

    Text Solution

    |

  4. The eccentric angles of extremities of a chord of an ellipse (x^2)/(a^...

    Text Solution

    |

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

    Text Solution

    |

  6. If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |

  7. If P Q R is an equilateral triangle inscribed in the auxiliary circle ...

    Text Solution

    |

  8. On the ellipse 4x^(2)+9y^(2)=1, the points at which the tangent are pa...

    Text Solution

    |

  9. Tangents are drawn to the ellipse 3x^2 + 5y^2 = 32 and 25x^2 +9y^2 = 4...

    Text Solution

    |

  10. Let two perpendicular chords of the ellipse (x^2)/(a^2) + (y^2)/(b^2) ...

    Text Solution

    |

  11. An ellipse passes through the point (4,-1) and touches the line x+4...

    Text Solution

    |

  12. Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(...

    Text Solution

    |

  13. The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2...

    Text Solution

    |

  14. If P(theta1) and D(theta2) be the end, points of two semi-conjugate di...

    Text Solution

    |

  15. If CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) +...

    Text Solution

    |

  16. CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^...

    Text Solution

    |

  17. The maximum distance of the centre of the ellipse (x^(2))/(16) +(y^(2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |