Home
Class 12
MATHS
Show that the tangents at the ends of co...

Show that the tangents at the ends of conjugate diameters of the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` intersect on the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=2`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Example|4 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|18 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 area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

If CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , then CP^(2) + CD^(2) =

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

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , The locus of the mid-point of PD, is

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1

The eccentric angles of the ends of L.R. of the ellipse (x^(2)/(a^(2))) + (y^(2)/(b^(2))) = 1 is

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

the equation of a diameter conjugate to a diameter y=(b)/(a)x of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

ARIHANT MATHS ENGLISH-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Show that the tangents at the ends of conjugate diameters of the ellip...

    Text Solution

    |

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

    Text Solution

    |

  3. about to only mathematics

    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. about to only mathematics

    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. Find the equation of an ellipse hose axes lie along the coordinate ...

    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=16s...

    Text Solution

    |

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

    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

    |