Home
Class 11
MATHS
If P is any point on the hyperbola whose...

If `P` is any point on the hyperbola whose axis are equal, prove that `S PdotS^(prime)P=C P^2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|22 Videos
  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA ENGLISH|Exercise All Questions|113 Videos

Similar Questions

Explore conceptually related problems

If Sa n dS ' are the foci, C is the center, and P is a point on a rectangular hyperbola, show that S PxxS^(prime)P=(C P)^2dot

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot .

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot

In Figure, P , is any point on the chord B C of a circle such that A B=A P . Prove that C P=C Q .

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

The center of an ellipse is C and P N is any ordinate. Point A ,A ' are the endpoints of the major axis. Then find the value of (P N^2)/(A N)dotA^(prime)Ndot

If P is any point on the ellipse 9x^(2) + 36y^(2) = 324 whose foci are S and S'. Then, SP + S' P equals

A transvers axis cuts the same branch of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Pa n dP ' and the asymptotes at Q and Q ' . Prove that P Q=P ' Q ' and P Q^(prime)=P^(prime)Qdot

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

RD SHARMA ENGLISH-HYPERBOLA-All Questions
  1. Find the equation of the hyperbola, referred to its principal axes o...

    Text Solution

    |

  2. Show that the equation x^2-2y^2-2x+8y-1=0 represents a hyperbola.

    Text Solution

    |

  3. If P is any point on the hyperbola whose axis are equal, prove that...

    Text Solution

    |

  4. Find the equation of the hyperbola whose conjugate axis is 5 and th...

    Text Solution

    |

  5. The foci of a hyperbola coincide with the foci of the ellipse (x^2)...

    Text Solution

    |

  6. If the distance between the foci of a hyperbola is 16 and its eccen...

    Text Solution

    |

  7. The equation of the directrix of a hyperbola is x-y+3=0. Its focus is ...

    Text Solution

    |

  8. Find the equation of the hyperbola whose : focus is (0,3) directrix is...

    Text Solution

    |

  9. Find the equation of the hyperbola whose : focus is (1,1) directrix is...

    Text Solution

    |

  10. Find the equation of the hyperbola whose : focus is (1,1) directrix is...

    Text Solution

    |

  11. Find the equation of the hyperbola whose : focus is (2,-1) directrix i...

    Text Solution

    |

  12. Find the equation of the hyperbola whose : focus (a ,0) , directrix is...

    Text Solution

    |

  13. Find the equation of the hyperbola whose : focus is (2,2) directrix is...

    Text Solution

    |

  14. Find the eccentricity, coordinates of the foci ,equations of directric...

    Text Solution

    |

  15. Find the eccentricity, coordinates of the foci, equations of directric...

    Text Solution

    |

  16. Find the eccentricity, coordinates of the foci ,equations of directric...

    Text Solution

    |

  17. Find the eccentricity, coordinates of the foci, equations of directric...

    Text Solution

    |

  18. Find the eccentricity, coordinates of the foci, equations of directric...

    Text Solution

    |

  19. Find the axes, eccentricity, latus rectum and the coordinates of the ...

    Text Solution

    |

  20. Find the centre, eccentricity, foci and directrices of the hyperbola :...

    Text Solution

    |