Home
Class 12
MATHS
A tangent drawn to the curve y=f(x) at P...

A tangent drawn to the curve `y=f(x)` at `P(x,y)` cuts the x-axis and y-axis at `A` and `B` respectively such that `BP:AP=2:1`. Given that `f(1)=1`. Answer the question: The curve passes through the point (A) `(2,1/4)` (B) `(2,1/2)` (C) `(2,1/8)` (D) none of these

A

equation of curve is `x dy/dx -3y = 0`

B

normal at (1, 1) is x `x+3y = 4`

C

curve passes through `(2, 1/8)`

D

equation of curve is `xdy/dx+3y=0`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    FIITJEE|Exercise Comprehension|8 Videos

  • APPLICATION OF DERIVATIVE

    FIITJEE|Exercise MATCH THE COLUMNS|4 Videos

  • APPLICATION OF DERIVATIVE

    FIITJEE|Exercise Assignment Objective (level-1)|52 Videos

  • AREA

    FIITJEE|Exercise Numerical Based|3 Videos

Similar Questions

Explore conceptually related problems

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:Equation of curve is (A) y=1/x (B) y=1/x^2 (C) y=1/x^3 (D) none of these

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:Equation of normal to curve at (1,1) is (A) x-4y+3=0 (B) x-3y+2=0 (C) x-2y+1=0 (D) none of these

A tangent drawn to the curve y = f(x) at P(x, y) cuts the x and y axes at A and B, respectively, such that AP : PB = 1 : 3. If f(1) = 1 then the curve passes through (k,(1)/(8)) where k is

Tangent is drawn at any point P of a curve which passes through (1,1) cutting x -axis and y -axis at A and B respectively.If AP:BP=3:1, then

If f'(x)=x-1, the equation of a curve y=f(x) passing through the point (1,0) is given by

A normal is drawn at a point P(x,y) of a curve.It meets the x-axis and the y-axis in point A AND B, respectively,such that (1)/(OA)+(1)/(OB)=1, where O is the origin.Find the equation of such a curve passing through (5,4)

A curve y=f(x) passes through (1,1) and tangent at P(x , y) cuts the x-axis and y-axis at A and B , respectively, such that B P : A P=3, then (a) equation of curve is x y^(prime)-3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2, 8 (d) equation of curve is x y^(prime)+3y=0

A curve y=f(x) passes through (1,1) and tangent at P(x,y) on it cuts x- axis and y-axis at A and B respectively such that BP:AP=3:1 then the differential equation of such a curve is lambda xy'+mu y=0 where ( mu + lambda -lambda^(2) ) / (mu - 2 lambda) is . Where mu and lambda are relatively prime natural

A normal is drawn at a point P(x,y) on a curve.It meets the x-axis and thedus ofthe director such that (x intercept) ^(-1)+(y- intercept) ^(-1)=1, where O is origin,the curve passing through (3,3).

FIITJEE-APPLICATION OF DERIVATIVE-Assignment Objective (level-2)
  1. If the equation x^(5) - 10 a^(3)x^(2) + b^(4)x + c ^(5) = 0 has three...

    Text Solution

    |

  2. A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-ax...

    Text Solution

    |

  3. The function f(x) = x^(2) + gamma / x has a

    Text Solution

    |

  4. If x = 1/2 and if (1-2x)/ (1-x+ x^(2)) + (2x-4x^(3))/ (1-x^(2) + x^(4)...

    Text Solution

    |

  5. Let f(x)=(x^(2)+)1)/([x]),1 lt x le 3.9.[.] denotes the greatest integ...

    Text Solution

    |

  6. Which of the following are / is true

    Text Solution

    |

  7. If f: R rightarrow R, f(x) is a differentiable bijective function , th...

    Text Solution

    |

  8. Let f(x) = x^(3) - 6x^(2) + 15x + 3. Then

    Text Solution

    |

  9. Let f(x) be a nonzero function whose all successive derivative exist ...

    Text Solution

    |

  10. The function f(x) = tan ^(-1)x -x decreases in the interval

    Text Solution

    |

  11. f(x) = e^(sinx+cosx) is an increasing function in

    Text Solution

    |

  12. Which of the following statements are true where phi(x) is a polynomi...

    Text Solution

    |

  13. The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

    Text Solution

    |

  14. Which of the following is/are true, (you may use f(x) = In(In x)/(Inx)

    Text Solution

    |

  15. If f(x) is continuous function , then

    Text Solution

    |

  16. If f(x) = (tan^-1 x)^2+2/(sqrt(x^2+1) then f is increasing in

    Text Solution

    |

  17. h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...

    Text Solution

    |

  18. If f(x)=overset(x)underset(0)int(sint)/(t)dt,xgt0, then

    Text Solution

    |

  19. Let f(x) = 5x tanx + 8 sin(tan x) + In(cos x) then in the interval (-...

    Text Solution

    |

  20. If thetain[-(pi)/9,-(pi)/(36)] such that f(theta)=tan(theta+(5pi)/(18)...

    Text Solution

    |