Home
Class 12
MATHS
The tangent at a point P(theta) to the e...

The tangent at a point `P(theta)` to the ellipse `x^2/a^2+y^2/b^2=1` cuts the auxilliary circle at Q and R. If QR subtend a right angle at C (centre) then show that `e=1/sqrt(1+sin^2 theta)`

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-I|52 Videos

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-II|68 Videos

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE 4.3 (VERY SHORT ANSWER QUESTIONS)|4 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

Similar Questions

Explore conceptually related problems

The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

The length of the subtangent (if exists) at any point theta on the ellipse x^2/a^2+y^2/b^2=1 is

The equation of the tangent at a point theta=3pi//4 to the ellipse x^(2)//16+y^(2)//9=1 is

The normal at a poitn P( theta) on the ellipse 5x^(2) +14y^(2) =70 cuts the curve again at a point Q (2theta) then "cos" theta

The tangent at 'p' on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the major axis in T and PN is the perpendicular to the x-axis, C being centre then CN.CT =

The slope of a common tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 and a concentric circle of radius r is

The equation of the tangent at the point theta=(pi)/(3) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 is

Find the equation of tangent at the point theta=(pi)/(3) to the ellipse (x^(2))/(9)+(y^(2))/(4) = 1

AAKASH SERIES-ELLIPSE-ADDITIONAL EXERCISE
  1. If the normal at any point P on the ellipse meets the axes in G and g ...

    Text Solution

    |

  2. Show that the area of a triangle inscribed in an ellipse bears a const...

    Text Solution

    |

  3. The tangent at a point P(theta) to the ellipse x^2/a^2+y^2/b^2=1 cuts ...

    Text Solution

    |

  4. If foci and the ends of the minor axis of an ellipse are the vertices ...

    Text Solution

    |

  5. Prove that the locus of an end of latusrectum of all ellipses having a...

    Text Solution

    |

  6. Show that the length of common tangent to the ellipse 'x^(2)/(25)+y^(2...

    Text Solution

    |

  7. Let d be the perpendicular distance from the centre of the ellipse x^(...

    Text Solution

    |

  8. Find the point on the curve 4x^(2) + a^(2)y^(2) = 4a^(2), 4lta^(2)lt8,...

    Text Solution

    |

  9. Prove that in an ellipse the perpendicular from focus upon any tangent...

    Text Solution

    |

  10. Let P be a point on the ellipse Let the line parallel to y-axis passin...

    Text Solution

    |

  11. Let P be a point on the ellipse Let the line parallel to y-axis passin...

    Text Solution

    |

  12. Consider the family of circles If in the 1st quadrant, the common tang...

    Text Solution

    |

  13. Show that the maximum distance of centre of the ellipse x^(2)/a^(2)+y^...

    Text Solution

    |

  14. The product of the perpendiculars from the foci on any tangent to the...

    Text Solution

    |

  15. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

    Text Solution

    |

  16. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

    Text Solution

    |

  17. Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and ...

    Text Solution

    |

  18. Given the base of the triangle and the sum of tangent of base angles a...

    Text Solution

    |

  19. If a circle intercepts the ellipse at four points, show that the sum o...

    Text Solution

    |

  20. If a line is drawn through a point A(3,4) to cut the circle x^(2)+y^(2...

    Text Solution

    |