Home
Class 11
MATHS
The sum of the squares of the perpendicu...

The sum of the squares of the perpendiculars on any tangents to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` from two points on the minor axis each at a distance `a e` from the center is
(a)`2a^2` (b) `2b^2` (c) `a^2+b^2` `a^2-b^2`

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

The sum of the squares of the perpendiculars on any tangent to the ellipse a 2 x 2 ​ + b 2 y 2 ​ =1 from two points on the minor axis, each at a distances ae from the centre, is

The sum fo the squares of the perpendicular on any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from two points on the mirror axis, each at a distance sqrt(a^(2) - b^(2)) from the centre, is

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

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

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 perpendicular from the foci on any tangent to the ellips (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is equal to b^(2)

The locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

The locus of the point of intersection of the perpendicular tangents to the circle x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b" is "

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

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equation of the ellipse (referred to its axes as the axes o...

    Text Solution

    |

  2. Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points who...

    Text Solution

    |

  3. The sum of the squares of the perpendiculars on any tangents to the ...

    Text Solution

    |

  4. A rod of length 12 cm moves with its ends always touching the coord...

    Text Solution

    |

  5. Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4, ...

    Text Solution

    |

  6. If alpha-beta= constant, then the locus of the point of intersection o...

    Text Solution

    |

  7. Two circles are given such that one is completely lying inside the ...

    Text Solution

    |

  8. How many real tangents can be drawn from the point (4, 3) to the hy...

    Text Solution

    |

  9. For an ellipse x^2/9+y^2/4=1 with vertices A and A', drawn at the poin...

    Text Solution

    |

  10. The first artificial satellite to orbit the earth was Sputnik I. It...

    Text Solution

    |

  11. Which of the following can be slope of tangent to the hyperbola 4x^2-y...

    Text Solution

    |

  12. A tangent to the ellipes x^2/25+y^2/16=1 at any points meet the line x...

    Text Solution

    |

  13. Tangents are drawn to the hyperbola 3x^2-2y^2=25 from the point (0,5/2...

    Text Solution

    |

  14. Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f1,0)a n d...

    Text Solution

    |

  15. From the center C of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , perpendicul...

    Text Solution

    |

  16. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  17. A common tangent to 9x^2-16y^2 = 144 and x^2 + y^2 = 9, is

    Text Solution

    |

  18. Find the equation of tangents to the curve 4x^2-9y^2=1 which are paral...

    Text Solution

    |

  19. Find the equation of the locus of the middle points of the chords of ...

    Text Solution

    |

  20. Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2...

    Text Solution

    |