Home
Class 11
MATHS
A variable chord of the hyperbola (x^2)/...

A variable chord of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1,(b > a),` subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

if the chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

if the chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

If the chord xcosalpha+ysinalpha=p of the hyperbola (x^2)/(16)-(y^2)/(18)=1 subtends a right angle at the center, and the diameter of the circle, concentric with the hyperbola, to which the given chord is a tangent is d , then the value of d/4 is__________

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

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.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. The equation |sqrt(x^2+(y-1)^2)-sqrt(x^2+(y+1)^2)|=K will represent a ...

    Text Solution

    |

  2. The exhaustive set value of alpha^2 such that there exists a tangent t...

    Text Solution

    |

  3. A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), s...

    Text Solution

    |

  4. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

    Text Solution

    |

  5. For which of the hyperbolas, can we have more than one pair of perpe...

    Text Solution

    |

  6. If (5, 12) and (24, 7) are the foci of an ellipse passing through t...

    Text Solution

    |

  7. If (5,12)a n d(24 ,7) are the foci of a hyperbola passing through the ...

    Text Solution

    |

  8. Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 t...

    Text Solution

    |

  9. If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four poi...

    Text Solution

    |

  10. If the foci of (x^2)/(a^2)-(y^2)/(b^2)=1 coincide with the foci of (x^...

    Text Solution

    |

  11. The locus of a point whose chord of contact with respect to the circle...

    Text Solution

    |

  12. The equation (x^2)/(1-r)-(y^2)/(1+r)=1,r >1, represents (a)an ell...

    Text Solution

    |

  13. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

    Text Solution

    |

  14. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

    Text Solution

    |

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

    Text Solution

    |

  16. If L is the length of the latus rectum of the hyperbola for which x=3a...

    Text Solution

    |

  17. If the chord xcosalpha+ysinalpha=p of the hyperbola (x^2)/(16)-(y^2)/(...

    Text Solution

    |

  18. If the vertex of a hyperbola bisects the distance between its center ...

    Text Solution

    |

  19. If the distance between two parallel tangents having slope m drawn to ...

    Text Solution

    |

  20. The area of triangle formed by the tangents from the point (3, 2) to t...

    Text Solution

    |