Home
Class 11
MATHS
Statement 1 : For the ellipse (x^2)/5+(y...

Statement 1 : For the ellipse `(x^2)/5+(y^2)/3=1` , the product of the perpendiculars drawn from the foci on any tangent is 3. Statement 2 : For the ellipse `(x^2)/5+(y^2)/3=1` , the foot of the perpendiculars drawn from the foci on any tangent lies on the circle `x^2+y^2=5` which is an auxiliary circle of the ellipse.

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 product of the perpendiculars drawn from the two foci of an ellipse to the tangent at any point of the ellipse 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

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)

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.

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y^2 -9 x^2 = 1 is

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y^2 -9 x^2 = 1 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

Number of tangent(s) which can be drawn to the ellipse 16 x^2+25 y^2=400 such that sum of perpendicular distance from the foci to the tangent is 8.

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

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1 : If there is exactly one point on the line 3x+4y+5sqrt...

    Text Solution

    |

  2. If the latus rectum of a hyperbola forms an equilateral triangle with ...

    Text Solution

    |

  3. Statement 1 : For the ellipse (x^2)/5+(y^2)/3=1 , the product of the p...

    Text Solution

    |

  4. If the latus rectum subtends a right angle at the center of the hyp...

    Text Solution

    |

  5. Statement 1 : The locus of the center of a variable circle touching...

    Text Solution

    |

  6. If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1...

    Text Solution

    |

  7. Statement 1 : A triangle A B C right-angled at A moves so that its per...

    Text Solution

    |

  8. Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-t...

    Text Solution

    |

  9. A ray emanating from the point (5, 0) is INCIDENT on the hyperbola 9x^...

    Text Solution

    |

  10. Statement 1 : If the line x+y=3 is a tangent to an ellipse with focie ...

    Text Solution

    |

  11. Normal is drawn at one of the extremities of the latus rectum of the ...

    Text Solution

    |

  12. Statement 1 : The area of the ellipse 2x^2+3y^2=6 is more than the are...

    Text Solution

    |

  13. An ellipse and a hyperbola are confocal (have the same focus) and the ...

    Text Solution

    |

  14. The point of intersection of the tangents at the point P on the ellips...

    Text Solution

    |

  15. The distance between two directrices of a rectangular hyperbola is 10 ...

    Text Solution

    |

  16. Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2= at th...

    Text Solution

    |

  17. Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1...

    Text Solution

    |

  18. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  19. Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1...

    Text Solution

    |

  20. A circle has the same center as an ellipse and passes through the foci...

    Text Solution

    |