Home
Class 12
MATHS
Prove that the chord of contact of tange...

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse
`x^(2)/a^(2)+y^(2)/b^(2)=1` will subtend a right angle at the centre, if
`h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)`

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS|Exercise Example|5 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 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

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is

Find the angle between the pair of tangents from the point (1,2) to the ellipse 3x^2+2y^2=5.

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot

If the tangents from the point (lambda, 3) to the ellipse x^2/9+y^2/4=1 are at right angles then lambda is

Tangents drawn from the point (4, 3) to the circle x^2+y^2-2x-4y=0 are inclined at an angle :

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse x^2/a^2+y^2/b^2=1 ,touches the circle x^2+y^2=c^2 , then the locus of the point ( α , β ) is

Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/4=1 touching the ellipse at point A and B. Q. The coordinates of A and B are

Find the locus of the points of the intersection of tangents to ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 which make an angle theta.

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 .

ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that the chord of contact of tangents drawn from the point (h,k)...

    Text Solution

    |

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

    Text Solution

    |

  3. Find the 17^(th) term in the following sequence whose n^(th) term is a...

    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. Find the 9^(th) term in the following sequence whose n^(th) term is an...

    Text Solution

    |

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

    Text Solution

    |

  8. The 5th, 8th, and 11th terms of a GP are p, q and s respectively. Find...

    Text Solution

    |

  9. Is 309 a term of the AP 11, 17, 23….?

    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 whose 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

    |