Home
Class 12
MATHS
Find the equations of the tangent and no...

Find the equations of the tangent and normal to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` at the point `(x0, y0).`

Text Solution

Verified by Experts

The correct Answer is:
`(x x_(0))/(a^(2))-(yy_(0))/(b^(2))=1,(y-y_(0))/(a^(2)y_(0))+(x-x_(0))/(b^(2)x_(0))=0`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.4|23 Videos

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.5|48 Videos

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.2|23 Videos

  • APPLICATION OF INTEGRALS

    NCERT BANGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at ( a sec, theta b tan theta) . Hence show that if the tangent intercepts unit length on each of the coordinate axis than the point (a,b) satisfies the equation x^(2)-y^(2)=1

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (asqrt(2),b) is ax+b sqrt(2)=(a^2+b^2)sqrt(2) .

Find the equations of the tangent and normal to the curve y=x^2-4x-5 at x= -2.

Find the equations of the tangent and normal to the curve x^(2/3)+y^((2)/(3))=2 at (1,1).

Find the equation of tangnets to the hyperbola (x^(2))/(25)-(y^(2))/(36)=1 , parallel to the line 3x-3y=0

Find the equation of the normal to the hyperbola x^(2)-y^(2)=9 at the point p(5,4).

Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1).

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

Find the equation of normal to the hyperbola 4x^(2)-9y^(2)=36 , at the point (1,2)

NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.3
  1. Find the equations of all lines having slope 0 which are tangent to th...

    Text Solution

    |

  2. Find points on the curve (x^(2))/(9) +(y^(2))/(16) =1 at which the tan...

    Text Solution

    |

  3. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  4. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  5. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  6. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  7. Find the equations of the tangent to the given curves at the indicated...

    Text Solution

    |

  8. Find the equation of the tangent line to the curve y = x^(2) – 2x +7 w...

    Text Solution

    |

  9. Show that the tangents to the curve y = 7x^(3) + 11 at the points wher...

    Text Solution

    |

  10. Find the points on the curve y = x^(3) at which the slope of the tange...

    Text Solution

    |

  11. For the curve y = 4x^(3) – 2x^(5) , find all the points at which the t...

    Text Solution

    |

  12. Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the t...

    Text Solution

    |

  13. Find the equation of the normal at the point (am^(2) ,am^(3) ) for the...

    Text Solution

    |

  14. Find the equation of the normals to the curve y = x^(3) + 2x + 6 which...

    Text Solution

    |

  15. Find the equations of the tangent and normal to the parabola y^(2) = 4...

    Text Solution

    |

  16. Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^...

    Text Solution

    |

  17. Find the equations of the tangent and normal to the hyperbola (x^(2))/...

    Text Solution

    |

  18. Find the equation of the tangent to the curve y= sqrt(3x-2) which is p...

    Text Solution

    |

  19. The slope of the normal to the curve y = 2x^(2) + 3 sin x at x = 0 is

    Text Solution

    |

  20. The line y = x + 1 is a tangent to the curve y^(2) = 4x at the point

    Text Solution

    |