Home
Class 11
MATHS
If alpha+beta=3pi , then the chord joini...

If `alpha+beta=3pi` , then the chord joining the points `alpha` and `beta` for the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` passes through which of the following points? Focus (b) Center One of the endpoints of the transverse exis. One of the endpoints of the conjugate exis.

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

If alpha-beta is constant prove that the chord joining the points alpha and beta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 touches a fixed ellipse

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 4

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

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 subtends a right angle at the vertex A(a ,0), then prove that tan(a/2)tan(beta/2)=-(b^2)/(a^2)dot

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

If alpha and beta are two points on the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 and the chord joining these two points passes through the focus (ae, 0) then e cos ""(alpha-beta)/(2)=

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

If the ratio of transverse and conjugate axis of the hyperbola x^2 / a^2 - y^2 / b^2 = 1 passing through the point (1, 1) is 1/3 , then its equation is

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

If P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that alpha-beta=2theta (a constant), then PQ touches the hyperbola

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0...

    Text Solution

    |

  2. Find the co-ordinates of all the points P on the ellipse, x^2/a^2+y^2/...

    Text Solution

    |

  3. If alpha+beta=3pi , then the chord joining the points alpha and beta f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If a point (x1,y1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1...

    Text Solution

    |

  8. Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and le...

    Text Solution

    |

  9. Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four poi...

    Text Solution

    |

  10. Find the coordinates of the foci  and the centre of the hyperbola ((...

    Text Solution

    |

  11. show that the area of the triangle inscribed in the circle x^(2)/a^(2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Statement 1 : The equations of tangents to the hyperbola 2x^2-3y^2=...

    Text Solution

    |

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

    Text Solution

    |

  17. If P=(x , y),F1=(3,0),F2=(-3,0), and 16 x^2+25 y^2=400 , then P F1+P F...

    Text Solution

    |

  18. Statement 1 : Every line which cuts the hyperbola x^2/4-y^2/16=1 at ...

    Text Solution

    |

  19. Find the equation of the hyperbola whose foci are (8,3)a n d(0,3) and ...

    Text Solution

    |

  20. The number of values of c such that the straight line y=4x+c touches t...

    Text Solution

    |