Home
Class 11
MATHS
If F1 and F2 are the feet of the per...

If `F_1` and `F_2` are the feet of the perpendiculars from the foci `S_1a n dS_2` of the ellipse `(x^2)/(25)+(y^2)/(16)=1` on the tangent at any point `P` on the ellipse, then prove that `S_1F_1+S_2F_2geq8.`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

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.

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

The locus of the point of intersection of two perpendicular tangents to the ellipse (x^(2))/(9) +(y^(2))/(4)=1 is -

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

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

Prove that SP + S'P = 20 for the ellipse (x^(2))/(100) + (y^(2))/(36) = 1 , S and S' are the two foci of the ellipse and P is any point on the ellipse

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide, then find the value of b^2

Find the length of chord of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 , whose middle point is ((1)/(2),(2)/(5)) .

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. An arc of a bridge is semi-elliptical with the major axis horizonta...

    Text Solution

    |

  18. An ellipse has O B as the semi-minor axis, F and F ' as its foci, ...

    Text Solution

    |

  19. P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' ...

    Text Solution

    |

  20. Prove that the curve represented by x=3(cost+sint),y=4(cost-sint),t in...

    Text Solution

    |