Home
Class 11
MATHS
Find the equations to the common tangent...

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`

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 equations (s) to common tangent (s) to the two hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 " and " y^(2)/a^(2) - x^(2)/b^(2) = 1 is /are

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

The slopes of the common tangents of the hyperbolas (x^(2))/(9)-(y^(2))/(16)=1 and (y^(2))/(9)-(x^(2))/(16)=1 , are

Find the equations of the tangent and normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . at the point (x_0,y_0)

Find the equation of the tangent to the curve (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,\ y_1) on it.

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

The equation of common tangent to the parabola y^2 =8x and hyperbola 3x^2 -y^2=3 is

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the equations of the tangents to the hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/( b ^(2)) = 1 are mutually perpendicular, show that the locus of P is the circle x ^(2) + y ^(2) =a ^(2) -b ^(2).

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Let aa n db be nonzero real numbers. Then the equation (a x^2+b y^2+c)...

    Text Solution

    |

  2. x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will represent ellipse if r lies in the...

    Text Solution

    |

  3. Find the equations to the common tangents to the two hyperbolas (x^2)/...

    Text Solution

    |

  4. A parabola is drawn with focus at one of the foci of the ellipse (x^2)...

    Text Solution

    |

  5. Let P(6,3) be a point on the hyperbola x^2/a^2-y^2/b^2=1If the normal ...

    Text Solution

    |

  6. Find the equation of the common tangent to the curves y^2=8x and xy=-1...

    Text Solution

    |

  7. If the maximum distance of any point on the ellipse x^2+2y^2+2x y=1 f...

    Text Solution

    |

  8. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2...

    Text Solution

    |

  9. Let Pi and Pi ' be the feet of the perpendiculars drawn from the foci ...

    Text Solution

    |

  10. An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The ecc...

    Text Solution

    |

  11. The number of points on the ellipse (x^2)/(50)+(y^2)/(20)=1 from which...

    Text Solution

    |

  12. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

    Text Solution

    |

  13. The equation of the ellipse whose axes are coincident with the coor...

    Text Solution

    |

  14. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

    Text Solution

    |

  15. An ellipse with major and minor axes lengths 2a and 2b , respectively,...

    Text Solution

    |

  16. Consider the hyperbola H, x^(2)-y^(2)=1 and a circle S with centre N(x...

    Text Solution

    |

  17. Let d be the perpendicular distance from the centre of the ellipse x^2...

    Text Solution

    |

  18. From a point P(1, 2), pair of tangents are drawn to hyperbola, one tan...

    Text Solution

    |

  19. A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P ...

    Text Solution

    |

  20. The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^...

    Text Solution

    |