Home
Class 11
MATHS
If two distinct tangents can be drawn fr...

If two distinct tangents can be drawn from the Point `(alpha,2)` on different branches of the hyperbola `x^2/9-y^2/(16)=1` then (1) `|alpha| lt 3/2` (2) `|alpha| gt 2/3` (3)`|alpha| gt 3` (4) `alpha =1`

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 two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

If from the point (alpha,alpha^2) two tangents drawn to any one branch of hyperbola x^2-4y^2=1 , then :

If two tangents can be drawn the different branches of hyperbola (x^(2))/(1)-(y^(2))/(4) =1 from (alpha, alpha^(2)) , then

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 is

Two tangents are drawn from a point (-4, 3) to the parabola y^(2)=16x . If alpha is the angle between them, then the value of cos alpha is

Two tangents are drawn from a point on hyperbola x^(2)-y^(2)=5 to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 . If they make angle alpha and beta with x-axis, then

If two tangents drawn from the point (alpha,beta) to the parabola y^2=4x are such that the slope of one tangent is double of the other, then prove that alpha=2/9beta^2dot

If two tangents drawn from the point (alpha,beta) to the parabola y^2=4x are such that the slope of one tangent is double of the other, then prove that alpha=2/9beta^2 .

The set of values of alpha for which the point (alpha,1) lies inside the curves c_1: x^2+y^2-4=0 and c_2: y^2=4x is (a) |alpha| < sqrt(3) (b) |alpha|<2 (c) 1/4 < alpha < sqrt(3) (d) none of these

Which of the following is independent of alpha in the hyperbola (0 lt alpha lt pi/2). x^2/cos^2 alpha-y^2/sin^2alpha=1

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

    Text Solution

    |

  2. Consider an ellipse E ,(x^2)/(a^2)+(y^2)/(b^2)=1 , centered at point O...

    Text Solution

    |

  3. If two distinct tangents can be drawn from the Point (alpha,2) on diff...

    Text Solution

    |

  4. Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then th...

    Text Solution

    |

  5. A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x...

    Text Solution

    |

  6. Rectangle ABCD has area 200.An ellipse with area 200pi passes through ...

    Text Solution

    |

  7. From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents a...

    Text Solution

    |

  8. The locus of the image of the focus of the ellipse (x^2)/(25)+(y^2)/9=...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. A point on the ellipse x^2+3y^2=37 where the normal is parallel to the...

    Text Solution

    |

  11. Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+...

    Text Solution

    |

  12. If a pair of variable straight lines x^2 + 4y^2+alpha xy =0 (where alp...

    Text Solution

    |

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

    Text Solution

    |

  14. The equation 3x^2+4y^2-18+16 y+43=k represents an empty set, if k<0 ...

    Text Solution

    |

  15. Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+...

    Text Solution

    |

  16. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

    Text Solution

    |

  17. If the sum of the slopes of the normal from a point P to the hyperbol...

    Text Solution

    |

  18. If the tangent at the point P(theta) to the ellipse 16 x^2+11 y^2=256 ...

    Text Solution

    |

  19. If the normal to the given hyperbola at the point (c t , c/t) meets th...

    Text Solution

    |

  20. If the equation of the ellipse is 3x^2+2y^2+6x-8y+5=0 , then which o...

    Text Solution

    |