Home
Class 11
MATHS
If two points are taken on the minor axi...

If two points are taken on the minor axis of an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is `2a^2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

The locus of the foot of the perpendicular from the centre of the ellipse x^2 +3y^2 =3 on any tangent to it is

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

The locus of points whose polars with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 are at a distance d from the centre of the ellipse, is

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (x1, y...

    Text Solution

    |

  2. Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

    Text Solution

    |

  3. If two points are taken on the minor axis of an ellipse (x^2)/(a^2)...

    Text Solution

    |

  4. If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts e...

    Text Solution

    |

  5. Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b...

    Text Solution

    |

  6. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

    Text Solution

    |

  7. If F1 and F2 are the feet of the perpendiculars from the foci S1a ...

    Text Solution

    |

  8. If the tangent at any point of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 m...

    Text Solution

    |

  9. Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=...

    Text Solution

    |

  10. A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=...

    Text Solution

    |

  11. If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) m...

    Text Solution

    |

  12. Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the...

    Text Solution

    |

  13. Find the locus of the middle points of all chords of (x^2)/4+(y^2)/...

    Text Solution

    |

  14. Tangents P Qa n dP R are drawn at the extremities of the chord of ...

    Text Solution

    |

  15. If the chords of contact of tangents from two poinst (x1, y1) and ...

    Text Solution

    |

  16. From the point A(4,3), tangent are drawn to the ellipse (x^2)/(16)...

    Text Solution

    |

  17. An ellipse is drawn with major and minor axis of length 10 and 8 resp...

    Text Solution

    |

  18. Find the foci of the ellipse 25(x+1)^2+9(y+2)^2=225.

    Text Solution

    |

  19. Find the equation of an ellipse whose axes are the x-and y-axis and...

    Text Solution

    |

  20. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

    Text Solution

    |