Home
Class 12
MATHS
If the normal at the point t1 to the rec...

If the normal at the point `t_1` to the rectangular hyperbola `xy=c^(2)` meets it again at the points `t_2` prove that `t_1^3t_2=-1`.

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -2|69 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

If the normal at point 't' of the curve xy = c^(2) meets the curve again at point 't'_(1) , then prove that t^(3)* t_(1) =- 1 .

The normal at P(ct,(c )/(t)) to the hyperbola xy=c^2 meets it again at P_1 . The normal at P_1 meets the curve at P_2 =

If the normal at (1,2) on the parabola y^(2)=4x meets the parabola again at the point (t^(2),2t) then the value of t is

If the normal to the rectangular hyperbola xy = c^2 at the point 't' meets the curve again at t_1 then t^3t_1, has the value equal to

If the normals drawn at the points t_(1) and t_(2) on the parabola meet the parabola again at its point t_(3) , then t_(1)t_(2) equals.

If the normal at(1, 2) on the parabola y^(2)=4x meets the parabola again at the point (t^(2), 2t) then the value of t, is

The normal drawn at a point (a t_1^2,-2a t_1) of the parabola y^2=4a x meets it again in the point (a t_2^2,2a t_2), then t_2=t_1+2/(t_1) (b) t_2=t_1-2/(t_1) t_2=-t_1+2/(t_1) (d) t_2=-t_1-2/(t_1)

If the normal to the rectangular hyperbola x y=c^2 at the point (c t ,c//t) meets the curve again at (c t^(prime),c//t '),t h e n t^3t^(prime)=1 (B) t^3t^(prime)=-1 (C) t.t^(prime)=1 (D) t.t^(prime)=-1

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -1
  1. If p1 and p2 be the lengths of perpendiculars from the origin on the ...

    Text Solution

    |

  2. In the curve x= a (cos t+ log tan(t/2)), y =a sin t. Show that the por...

    Text Solution

    |

  3. If the normal at the point t1 to the rectangular hyperbola xy=c^(2) me...

    Text Solution

    |

  4. The normal to the curve 5x^(5)-10x^(3)+x+2y+6 =0 at P(0, -3) meets the...

    Text Solution

    |

  5. If y=4x-5 is a tangent to the curve y^(2)=px^(3) +q at (2, 3), then

    Text Solution

    |

  6. The point on the curve y=x^(3) at which the tangent to the curve is pa...

    Text Solution

    |

  7. If the tangent at any point P on the curve x^m y^n = a^(m+n), mn != 0...

    Text Solution

    |

  8. Find the slope of the normal to the curve x = a cos^(3) theta, y = a s...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. Show the condition that the curves a x^2+b y^2=1 and Ax^2+By^2=1 shoul...

    Text Solution

    |

  11. The length of the normal to the curve y=a((e^(-x//a)+e^(x//a))/(2)) at...

    Text Solution

    |

  12. Find the angle of intersection of y=a^xa n dy=b^x

    Text Solution

    |

  13. Find the euation of normal to the curve x=a( cos theta + theta sin th...

    Text Solution

    |

  14. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

    Text Solution

    |

  15. The function x-(log(1+x)/x)(x>0) is increasing in:

    Text Solution

    |

  16. Let f(x) =cos (cos x). Then which one is not correct?

    Text Solution

    |

  17. Let f(x)=x-1/2 log (x^(2)+1). Then f' (x) is :

    Text Solution

    |

  18. The function f(x)=(x^(4)-42x^(2)-80x+32)^(3) is :

    Text Solution

    |

  19. Find the intervals in which f(x)=2\ log\ (x-2)-x^2+4x+1 is increasing ...

    Text Solution

    |

  20. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

    Text Solution

    |