Home
Class 12
MATHS
Tangents at right angle are drawn to the...

Tangents at right angle are drawn to the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1`. Show that the focus of the middle points of the chord of contact is the curve `(x^(2)/a^(2)+y^(2)/b^(2))^(2)=(x^(2)+y^(2))/(a^(2)+b^(2))`.

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise For Session 2|15 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

From a point O on the circle x^(2)+y^(2)=d^(2) tangents OP and OQ are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b). Show that the locus of the mid point of the chord PQ describes the curve x^(2)+y^(2)=d^(2)[(x^(2))/(a^(2))+(y^(2))/(b^(2))]^(2)

The locus of mid-points of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

Chords of the circle x^(2)+y^(2)=a^(2) toches the hyperbola x^(2)/a^(2)-y^(2)//b^(2)=1 . Prove that locus of their middle point is the curve (x^2 +y^2)^2=a^(2)x^(2)-b^(2)y^(2)

The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from a focus, is

The angle of intersection of the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and x^(2)+y^(2)=ab, is

The distance of the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 from a focus is

Find the equation of the tangent at the point (x,y) of the curve : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Tangents are drawn from any point on the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 to the circle x^(2)+y^(2)=9 .If the locus of the mid-point of the chord of contact is a a(x^(2)+y^(2))^(2)=bx^(2)-cy^(2) then the value of (a^(2)+b^(2)+c^(2))/(7873)

Tangent are drawn from the point (3,2) to the ellipse x^(2)+4y^(2)=9. Find the equation to their chord of contact and the middle point of this chord of contact.

ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Tangents at right angle are drawn to the ellipse x^(2)/a^(2)+y^(2)/b^(...

    Text Solution

    |

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

    Text Solution

    |

  3. Find the equation of the common tangent in the 1st quadrant to the cir...

    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. Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the...

    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. Equation of the ellipse whose axes are the axes of coordinates and ...

    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=16...

    Text Solution

    |

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

    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

    |