Home
Class 12
MATHS
P is a point on the ellipse (x^(2))/(a^(...

P is a point on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` S and `S^(1)` are foci A & `A^(1)` are the vertices of the ellipse then the ratio `|(SP-S^(1)P)/(SP+S^(1)P)|` is

A

e cos `theta`

B

`e^(2) cos theta`

C

`e^(3) cos theta`

D

`(1)/(e ) cos theta`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    AAKASH SERIES|Exercise EXERCISE-II|68 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos
  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

Similar Questions

Explore conceptually related problems

P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 ; S,S^(1) are the Foci of the ellipse then SP + S^(1)P =

If P is a point on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 whose foci are S, S^(') " then "PS+PS^(')=

P((pi)/(6)) is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 S,S^(1) are foci of ellipse then |SP-S^(1)P|=

If P is a point on the e llip (x^(2))/(36)+(y^(2))/(9)=1 , S and S ’ are the foci of the ellipse then find SP + SP^1

P is a point on the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1 with foci at S, S^(-1). Normal at P cuts the x-axis at G and (SP)/( S^(1)P) =(2)/(3) then (SG)/( S^(1)G)

Let 'P' be a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S (ae , 0) and S'(-ae,0) . If A is the area of the triangle PSS' , then the maximum value of A (where e is eccentricity and b^(2)=a^(2)(1-e^(2))) is

Let d be the perpendicular distance from the centre of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 to the tangent drawn at a point P on ellipse. If F_(1) and F_(2) are the foci of the ellipse, then show that (PF_(1)-PF_(2))^(2)=4a^(2)(1-(b^(2))/(d^(2)))

Let S, S' be the focii and B, B' be the minor axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if angle BSS'= theta and eccentrictiy of the ellipse is e, then show that e=cos theta

Let P be a variable point on the ellipse (x^(2))/(25)+(y^(2))/(16)=1 with foci at S and S'. Then find the maximum area of the triangle SPS'

AAKASH SERIES-ELLIPSE-PRACTICE EXERCISE
  1. The equation of the normal to the ellipse x^(2)/4+y^(2)/1=1 at (2, -1)...

    Text Solution

    |

  2. The equations of the tangents drawn from (2, 3) to the ellipse 9x^(2) ...

    Text Solution

    |

  3. If a gt b and e is the eccentricity of the ellipse then the equation ...

    Text Solution

    |

  4. If the normal at one end of latusrectum of an ellipse (x^(2))/(a^(2))...

    Text Solution

    |

  5. The equation to the locus of point of intersection of lines y-mx=sqr...

    Text Solution

    |

  6. The number of tangents that can be drawn to an ellipse perpendicular t...

    Text Solution

    |

  7. If the chords of contact of tangents from two points to the ellipse ar...

    Text Solution

    |

  8. The mid point of the chord 3x - 2y + 8 = 0 of the ellipse 3x^(2) + 4y^...

    Text Solution

    |

  9. The distance of a point on the ellipse x^(2) + 3y^(2) = 6 from its cen...

    Text Solution

    |

  10. The equation of the tangent at a point theta=3pi//4 to the ellipse x^(...

    Text Solution

    |

  11. The equation of the normal to the ellipse at the point whose eccentri...

    Text Solution

    |

  12. P is a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 S and S...

    Text Solution

    |

  13. If the chord joining two points whose eccentric angles are alpha and ...

    Text Solution

    |

  14. If alpha and beta are the eccentric angles of the ends of a focal chor...

    Text Solution

    |

  15. The minimum area of triangle formed by the tangent to the ellipse (x^(...

    Text Solution

    |

  16. If a tangent to the ellipse meets major and minor axis at M and N resp...

    Text Solution

    |

  17. The locus of the variable point P for which the chord of contact of to...

    Text Solution

    |

  18. If pi+theta is the eccentric angle of a point on the ellipse 16x^(2)+2...

    Text Solution

    |

  19. The locus of midpoints of chords of the ellipse x^(2)//a^(2)+y^(2)//b^...

    Text Solution

    |

  20. If y = mx + c is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |