Home
Class 11
MATHS
If a x+b y=1 is tangent to the hyperbola...

If `a x+b y=1` is tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , then `a^2-b^2` is equal to (A) `1/(a^2e^2)` (B) `a^2e^2` (C) `b^2e^2` (D) none of these

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

Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

If the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=-1 is (5)/(4) , then b^(2) is equal to

If the eccentricity of the hyperbola conjugate to the hyperbola (x^2)/(4)-(y^2)/(12)=1 is e, then 3e^2 is equal to:

Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to 5 (b) 25 (c) 16 (d) none of these

A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to 5 (b) 25 (c) 16 (d) none of these

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

The value of int_1^e((x/e)^(2x)+(e/x)^x)log_ex dx is equal to (A) e-1/(2e^2)-1/2 (B) e-1/(2e^2)+1/2 (C) e^3-1/(2e^2)-1/2 (D) none of these

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If tangents drawn from the point (a ,2) to the hyperbola (x^2)/(16)-(y...

    Text Solution

    |

  2. If the hyperbola x^2-y^2=4 is rotated by 45^0 in the anticlockwise dir...

    Text Solution

    |

  3. Find the point on the hyperbola x^2/24 - y^2/18 = 1 which is nearest t...

    Text Solution

    |

  4. The number of possible tangents which can be drawn to the curve 4x^2-9...

    Text Solution

    |

  5. If values of a, for which the line y=ax+2sqrt(5) touches the hyperbola...

    Text Solution

    |

  6. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

    Text Solution

    |

  7. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

    Text Solution

    |

  8. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

    Text Solution

    |

  9. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

    Text Solution

    |

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

    Text Solution

    |

  11. Locus of the feet of the perpendiculars drawn from either foci on a va...

    Text Solution

    |

  12. The locus of the foot of the perpendicular from the center of the hy...

    Text Solution

    |

  13. If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4, then the po...

    Text Solution

    |

  14. Which of the following is independent of alpha in the hyperbola (0 ...

    Text Solution

    |

  15. Consider the graphs of y = Ax^2 and y^2 + 3 = x^2 + 4y, where A is a p...

    Text Solution

    |

  16. Tangents are drawn from the point (alpha, beta) to the hyperbola 3x^(2...

    Text Solution

    |

  17. The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+...

    Text Solution

    |

  18. If y=m x+c is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, havi...

    Text Solution

    |

  19. A(-2, 0) and B(2,0) are two fixed points and P 1s a point such that PA...

    Text Solution

    |

  20. Statement 1 : Given the base B C of the triangle and the radius ratio ...

    Text Solution

    |