Home
Class 12
MATHS
The tangent at a point P on the curve y ...

The tangent at a point P on the curve `y =ln ((2+ sqrt(4-x ^(2)))/(2- sqrt(4-x ^(2))))-sqrt(4-x ^(2))` meets the y-axis at T, then `PT^(2)` equals to :

A

2

B

4

C

8

D

16

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )|29 Videos

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos

  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK)|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

Show that the segment of the tangent to the curve y=(a)/(2)In((a+sqrt(a^(2)-x^(2)))/(a-sqrt(a^(2)-x^(2))))-sqrt(a^(2)-x^(2)) contained between the y= axis and the point of tangency has a constant length.

The portion of the tangent to the curve x=sqrt(a^(2)-y^(2))+(a)/(2)(log(a-sqrt(a^(2)-y^(2))))/(a+sqrt(a^(2)-y^(2))) intercepted between the curve and x -axis,is of legth.

log_(2)sqrt(x)+log_(2)sqrt(x)=4

If y=log(x^(2)+sqrt(x^(4)-a^(4)))," then "y_(1)sqrt(x^(4)-a^(4))=

The equation of the tangent to the curve y= int_(x^4)^(x^6) (dt)/( sqrt( 1+t^2) ) at x=1 is

log_(4)(x^(2)-1)-log_(4)(x-1)^(2)=log_(4)sqrt((4-x)^(2))

The point at which the tangent to the curve y=sqrt(4x-3)-10 has slope (2)/(3) is

VIKAS GUPTA (BLACK BOOK)-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The tangent at a point P on the curve y =ln ((2+ sqrt(4-x ^(2)))/(2- s...

    Text Solution

    |

  2. A conical vessel is to be prepared out of a circular sheet of gold of ...

    Text Solution

    |

  3. On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...

    Text Solution

    |

  4. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  5. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

    Text Solution

    |

  6. Find sum of all possible values of the real parameter b, if the differ...

    Text Solution

    |

  7. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  8. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  9. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  10. There is a point (p,q) on the graph of f(x)=x^2 and a point (r , s) on...

    Text Solution

    |

  11. f (x)= max |2 sin y-x| where y in R then determine the minimum value o...

    Text Solution

    |

  12. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  13. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

    Text Solution

    |

  14. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  15. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  16. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

    Text Solution

    |

  17. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  18. If f (x) is continous and differentiable in [3,9) and f'(x) in [-2,8] ...

    Text Solution

    |

  19. It is given that f 9x) is difined on R satisfyinf f (1)=1 and for AA ...

    Text Solution

    |

  20. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  21. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |