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

  • HYPERBOLA

    ARIHANT MATHS|Exercise JEE Type Solved Examples : Subjective Type Questions|1 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise For Session 1|19 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 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)

ARIHANT MATHS-HYPERBOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the ...

    Text Solution

    |

  2. The locus a point P(alpha,beta) moving under the condition that the li...

    Text Solution

    |

  3. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(...

    Text Solution

    |

  4. A hyperbola, having the transverse axis of length 2sin theta, is conf...

    Text Solution

    |

  5. Two braches of a hyperbola

    Text Solution

    |

  6. For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of ...

    Text Solution

    |

  7. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

    Text Solution

    |

  8. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  9. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

    Text Solution

    |

  10. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

    Text Solution

    |

  11. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

    Text Solution

    |

  12. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

    Text Solution

    |

  13. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

    Text Solution

    |

  14. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

    Text Solution

    |

  15. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

    Text Solution

    |

  16. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

    Text Solution

    |

  17. A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci a...

    Text Solution

    |

  18. If 2x-y+1=0 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(16)=1 the...

    Text Solution

    |