Home
Class 11
MATHS
The tangent at a point P on the hyperbol...

The tangent at a point P on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets one of the directrix at F. If PF subtends an angle `theta` at the corresponding focus, then `theta` =

A

`45^(@)`

B

`30^(@)`

C

`60^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|56 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • INEQUALITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos

Similar Questions

Explore conceptually related problems

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets one of the directrix at Fdot If P F subtends an angle theta at the corresponding focus, then theta= (a) pi/4 (b) pi/2 (c) (3pi)/4 (d) pi

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets one of the directrix at Fdot If P F subtends an angle theta at the corresponding focus, then theta= pi/4 (b) pi/2 (c) (3pi)/4 (d) pi

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

A tangent is drawn at any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 . If this tangent is intersected by the tangents at the vertices at points P and Q, then which of the following is/are true

If the tangent at the point (asec alpha, b tanalpha ) to the hyberbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 meets the transverse axis at T. Then the distances of T form a focus of the hyperbola is

The tangent at a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , which in not an extremely of major axis meets a directrix at T. Statement-1: The circle on PT as diameter passes through the focus of the ellipse corresponding to the directrix on which T lies. Statement-2: Pt substends is a right angle at the focus of the ellipse corresponding to the directrix on which T lies.

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from a focus, 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= (a) a^2(e^4 sec^2 theta-1) (b) a^2(e^4 tan^2 theta-1) (c) b^2(e^4 sec^2 theta-1) (d) b^2(e^4 sec^2 theta+1)

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

OBJECTIVE RD SHARMA ENGLISH-HYPERBOLA-Chapter Test
  1. If the tangent at (h, k) on b^2x^2-a^2y^2=a^2b^2 cuts the auxiliary ci...

    Text Solution

    |

  2. If the chords of contact of tangents drawn from P to the hyperbola x^(...

    Text Solution

    |

  3. The tangent at a point P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(...

    Text Solution

    |

  4. The mid-point of the chord intercepted by the hyperbola 9x^(2)-16y^(2)...

    Text Solution

    |

  5. Locus of P such that the chord of contact of P with respect to y^2=4ax...

    Text Solution

    |

  6. C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangen...

    Text Solution

    |

  7. If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2), then

    Text Solution

    |

  8. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

    Text Solution

    |

  9. The product of lengths of perpendicular from any point on the hyperbol...

    Text Solution

    |

  10. The angle between the asymptotes of the hyperbola 3x^(2)-y^(2)=3, is

    Text Solution

    |

  11. Find the area of the triangle formed by any tangent to the hyperbola (...

    Text Solution

    |

  12. If e1a n d\ e2 are respectively the eccentricities of the ellipse (x^2...

    Text Solution

    |

  13. The distance between the directrices of the hyperbola x=8s e ctheta,\ ...

    Text Solution

    |

  14. The straight line x+y=sqrt(2)p will touch the hyperbola 4x^(2)-9y^(2)=...

    Text Solution

    |

  15. The locus of the point of intersection of perpendicular tangents to th...

    Text Solution

    |

  16. .Find the product of lengths of the perpendiculars from any point on t...

    Text Solution

    |

  17. The angle between the asymptotes of the hyperbola 27x^(2)-9y^(2)=24, i...

    Text Solution

    |

  18. The equation of the chord of contact of tangents from (1,2) to the hyp...

    Text Solution

    |

  19. Equation of the hyperbola whose vertices are (+-3,0) and foci at (+-5,...

    Text Solution

    |

  20. The length of the semi-transverse axis of the rectangular hyperbola xy...

    Text Solution

    |