Home
Class 12
MATHS
Show that the normal to the rectangular ...

Show that the normal to the rectangular hyperbola `xy=c^(2)` at point t meet the curve again at t' such that `t^(3)t'=1`.

Promotional Banner

Topper's Solved these Questions

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise A MULTIPLE CORRECT ANSWER TYPE|5 Videos
  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise INTEGER ANSWER TYPE|5 Videos
  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|42 Videos
  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos
  • TRANSFORMATIONS OF SUMS AND PRODUCTS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

The slope of the normal to the rectangular hyperbola xy=4 "at" (2t, (2)/(t)) is -

The slope of the tangent to the rectangular hyperbola xy=c^(2) at the point (ct,(c)/(t)) is -

The slope of the normal to rectangular hyperbopla xy= 4 at (2t,2/t) is a) - t^2 b) t^2 c) 2t d)-2t

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.

Show that the normal at the point (3t,(4)/(t)) to the curve xy=12 cuts the curve again at the point whose parameter t_(1) is given by t_(1)=-(16)/(9t^(3))

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot

If the tangent at a point P, with parameter t, on the curve x=4t^(2)+3,y=8t^(3)-1,t in RR , meets the curve again at a point Q, then the coordinates of Q are

Find the eauation of the normal to the hyperbola xy=4 at the pint (2,2). Also ,determine the point at which the normal again intersects the hyperbola.

The slope of the tangent to the curve xy= c^2 at (ct,c/t) is

The gradient of normal at t = 2 of the curve x=t^(2)-3,y=2t+1 is -

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. The equation of the tangent to the curve y=a+bx+cx^() where it meet th...

    Text Solution

    |

  2. If x(1) and y(1) be the intercepts on the x and y-axis respectively of...

    Text Solution

    |

  3. Show that the length of the portion of the tangent to the curve x^((2)...

    Text Solution

    |

  4. Show that the sum of the intercept on the coordinates axes of tangent ...

    Text Solution

    |

  5. If h and k be the intercept on the coordinates axes of tangent to the ...

    Text Solution

    |

  6. Find the equation of the normal to the parabola y^(2)=4ax at a point (...

    Text Solution

    |

  7. Find the coodition that the straight line lx+my+n=0 is a normal to the...

    Text Solution

    |

  8. Find the coodition that the straight line lx+my+n=0 is a normal to the...

    Text Solution

    |

  9. If the line lx+my=1 be a normal to the hyperbola (x^(2))/(a^(2))-(y...

    Text Solution

    |

  10. If the striaht line lx+my=1 is a normal to the parbaola y^(2)=4ax then...

    Text Solution

    |

  11. If the line lx+my=1 is normal to the hyperbola (x^(2))/(9)-(y^(2))/(4)...

    Text Solution

    |

  12. Show that the line (ax)/(3)+(by)/(4)=c be a normal to the ellipse (x^2...

    Text Solution

    |

  13. If the line x cos alpha+ y sin alpha=p be a normal to the hyperbola b^...

    Text Solution

    |

  14. Show that the normal to the curve x=3 cos theta- cos^(2) theta, y= 3 s...

    Text Solution

    |

  15. Show that the normal at any point theta to the curve x=a(cos theta+ th...

    Text Solution

    |

  16. Show that the normal to the rectangular hyperbola xy=c^(2) at point t ...

    Text Solution

    |

  17. The angle between the two tangents drawn from a point p to the circle ...

    Text Solution

    |

  18. Find the equation of tangent to the curve xy^(2)=4(4-x) where it meet ...

    Text Solution

    |

  19. Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^...

    Text Solution

    |

  20. Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=...

    Text Solution

    |