Home
Class 12
MATHS
A normal to the hyperbola (x^(2))/(a^(2)...

A normal to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola `a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)`

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos

  • Elementary Probability

    A DAS GUPTA|Exercise Exercise|137 Videos

  • Equations, Inequation and Expressions

    A DAS GUPTA|Exercise Exercise|301 Videos

Similar Questions

Explore conceptually related problems

A normal to (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes in L and M . The perpendiculars to the axes through L and M intersect at P .Then the equation to the locus of P is

If the normal at 'theta' on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at G , and A and A' are the vertices of the hyperbola , then AC.A'G=

The line lx+my+n=0 will be a normal to the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) if

A tangent (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes at A and B.Then the locus of mid point of AB is

Ifthe normal at P the rectangular hyperbola x^(2)-y^(2)=4 meets the axes in G and g and C is the centre of the hyperbola,then

A tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its asymptotes at P and Q. If C its centre,prove that CP.CQ=a^(2)+b^(2)

A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(...

    Text Solution

    |

  2. Find the eccentric angle of a point on the ellipse x^2 + 3y^2 = 6 at a...

    Text Solution

    |

  3. Which of the following is an exterior point of the ellipse 16x^2+9y^2-...

    Text Solution

    |

  4. The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k is

    Text Solution

    |

  5. Find the equaiton of the tangents to the hyperbola x^2 - 2y^2 = 18 whi...

    Text Solution

    |

  6. A point on the ellipse x^2+3y^2=37 where the normal is parallel to the...

    Text Solution

    |

  7. if the ordinate of the point of contact be 2 then the equation of the ...

    Text Solution

    |

  8. A tangent to the ellipse 16x^2 + 9y^2 = 144 making equal intercepts o...

    Text Solution

    |

  9. If the tangent to the ellipse x^2 +4y^2=16 at the point 0 sanormal to ...

    Text Solution

    |

  10. An ellipse having foci (3,1) and (1, 1) passes through the point (1, 3...

    Text Solution

    |

  11. If P & Q are the ends of a pair of conjugate diameters & C is the cent...

    Text Solution

    |

  12. If any point on a hyperbola is (3 tantheta, 2sectheta) then eccentrici...

    Text Solution

    |

  13. If the normal to the rectangular hyperbola xy = c^2 at the point 't' m...

    Text Solution

    |

  14. Equation (2 + lambda)x^2-2 lambdaxy+(lambda -1)y^2-4x-2=0 represents a...

    Text Solution

    |

  15. Find the locus of the middle points of the normals chords of the recta...

    Text Solution

    |

  16. The line y=m x-((a^2-b^2)m)/(sqrt(a^2+b^2m^2)) is normal to the ellise...

    Text Solution

    |

  17. A rectangular hyperbola whose centre is C is cut by any circle of radi...

    Text Solution

    |

  18. A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the ...

    Text Solution

    |

  19. Let P be a point such that the sum of the slopes of normals drawn from...

    Text Solution

    |

  20. Let ABC be an equilateral triangle inscribed in the circle x^2+y^2=a^...

    Text Solution

    |