Home
Class 11
MATHS
If the normal at p(theta) on the hyperbo...

If the normal at `p(theta)` on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets the transverse axis at G, then prove that `AG*A'G=a^(2)(e^(4)sec^(2)theta-1),` where A and A' are the vertices of the hyperbola.

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

If the normal at P(theta) on the hyperbola (x^2)/(a^2)-(y^2)/(2a^2)=1 meets the transvers axis at G , then prove that A GdotA^(prime)G=a^2(e^4sec^2theta-1) , where Aa n dA ' are the vertices of the hyperbola.

If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

If x=a sin theta and y=b tan theta , then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1 .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If the normal at a point P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.

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

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Let L L ' be the latus rectum through the focus of the hyperbola (x^2)...

    Text Solution

    |

  2. Find the equation of the common tangent in the first quadrant of the c...

    Text Solution

    |

  3. If the normal at p(theta) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^...

    Text Solution

    |

  4. The eccentricity of the hyperbola whose latus rectum is 8 and conjugat...

    Text Solution

    |

  5. Prove that in an ellipse, the perpendicular from a focus upon any tang...

    Text Solution

    |

  6. Find the asymptotes of the curve xy-3y-2x=0.

    Text Solution

    |

  7. With one focus of the hyperbola x^2/9-y^2/16=1 as the centre, a circle...

    Text Solution

    |

  8. The equation of the passing through the of the ellipse (x^(2))/(16)+(y...

    Text Solution

    |

  9. Two circles are given such that they neither intersect nor touch. Then...

    Text Solution

    |

  10. lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3...

    Text Solution

    |

  11. An ellipse has O B as the semi-minor axis, Fa n dF ' as its foci...

    Text Solution

    |

  12. If A, B and C are three points on the hyperbola xy=c^(2) such that AB ...

    Text Solution

    |

  13. Statement 1 : If from any point P(x1, y1) on the hyperbola (x^2)/(a^2)...

    Text Solution

    |

  14. Consider the family of circles x^2+y^2=r^2, 2 < r < 5 . If in the fir...

    Text Solution

    |

  15. Prove that the locus of the point of intersection of the tangents at t...

    Text Solution

    |

  16. Number of points from where perpendicular tangents can be drawn to the...

    Text Solution

    |

  17. On which curve does the perpendicular tangents drawn to the hyperbola ...

    Text Solution

    |

  18. The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+...

    Text Solution

    |

  19. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

    Text Solution

    |

  20. If P(x ,y) is any point on the ellipse 16 x^2+25 y^2=400 and f1=(3,...

    Text Solution

    |