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

`e^(2)(1+cos^(2)theta)=1`

B

`e^(2)(cosec^(2)theta+1)=1`

C

`e^(2)(1+sin^(2)theta)=1`

D

`e^(2)(1+tan^(2)theta)=1`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|15 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 3|14 Videos

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

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

  • ESSENTIAL MATHEMATICAL TOOLS

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

Similar Questions

Explore conceptually related problems

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

From any point on any directrix of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,a > b , a pari of tangents is drawn to the auxiliary circle. Show that the chord of contact will pass through the correspoinding focus of the ellipse.

Find the locus of the mid point of the circle x^2+y^2=a^2 which subtend a right angle at the point (p,q)

The locus of the point, the chord of contact of which wrt the circle x^(2)+y^(2)=a^(2) subtends a right angle at the centre of the circle is

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (c ,0)dot

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0)dot

Two parallel tangents of a circle meet a third tangent at points P and Q. Prove that PQ subtends a right angle at the centre.

ARIHANT MATHS ENGLISH-ELLIPSE-Exercise (Single Option Correct Type Questions)
  1. If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |

  2. An arc of a bridge is semi-elliptical with the major axis horizonta...

    Text Solution

    |

  3. A tangent to the ellipse (x^2)/(25)+(y^2)/(16)=1 at any point P meets ...

    Text Solution

    |

  4. If tangents are drawn from any point on the circle x^(2) + y^(2) = 25...

    Text Solution

    |

  5. the equation of the chord of contact of the pair of tangents drawn to ...

    Text Solution

    |

  6. x-2y+4=0 is a common tangent to y^2=4x and x^4/4+y^2/b^2=1. Then the v...

    Text Solution

    |

  7. Find a point on the curve x^(2)+2y^(2)=6 whose distance from the line ...

    Text Solution

    |

  8. From a point on the axis of x common tangents are drawn to the parabol...

    Text Solution

    |

  9. If circumcentre of an equilateral triangle inscribed in x^(2)/a^(2) + ...

    Text Solution

    |

  10. A parabola is drawn whose focus is one of the foci of the ellipse x^2...

    Text Solution

    |

  11. If the maximum distance of any point on the ellipse x^2+2y^2+2x y=1 fr...

    Text Solution

    |

  12. The length of the common chord of the ellipse ((x-1)^2)/9+((y-2)^2)/4=...

    Text Solution

    |

  13. The eccentricity of ellipse ax^2 + by^2 + 2gx + 2fy + c = 0 if its axi...

    Text Solution

    |

  14. A circle has the same center as an ellipse and passes through the foci...

    Text Solution

    |

  15. The area of the rectangle formed by the perpendiculars from the centre...

    Text Solution

    |

  16. An ellipse is inscribed in a circle and a point within the circle is c...

    Text Solution

    |

  17. An ellipse slides between two perpendicular straight lines. Then id...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |