Home
Class 12
MATHS
What is the equation of the curve whose...

What is the equation of the curve whose slope any point is equal to 2x and which passes through the origin?

A

`y(1-x)=x^(2)`

B

`y^(2)(1+x^(2))=x^(4)`

C

`y^(2)=(x+1)^(2)`

D

`y=x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Slope at the point (x,y) =2x
`therefore (dy)/(dx)=2x`
Promotional Banner

Topper's Solved these Questions

  • 3-D GEOMETRY

    NDA PREVIOUS YEARS|Exercise MCQ|147 Videos

  • BINOMIAL THEROREM, MATHEMATICAL INDUCTION

    NDA PREVIOUS YEARS|Exercise MQS|65 Videos

Similar Questions

Explore conceptually related problems

Show that the equation of the curve whose slope at any point is equal to y+2x and which passes through the origin is y+2(x+1)=2e^(2x)

show that the equation of the curve whose slope at any point is equal to y+2x and which passes through the origin is y+2(x+1)=2e^(2x)

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^(x) - x-1) .

The equation of one of the curves whose slope at any point is equal to y+2x and y(0)=0 is

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x and which passes through the point (2,1) is x^2+2xy=8

NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
  1. What is the smallest value o fm for which f(x) =x^(2)+mx+5 is increasi...

    Text Solution

    |

  2. What is the maximum value o fx y subject to the condition x+y=8 ?

    Text Solution

    |

  3. What is the equation of the curve whose slope any point is equal to 2...

    Text Solution

    |

  4. What is the maximum value of the function logx-x?

    Text Solution

    |

  5. A rectanglular box with a cover is to have a square base. The volume i...

    Text Solution

    |

  6. f(x) = cos x is monotonic decreasing under which one of the following ...

    Text Solution

    |

  7. What is the minimum value of 2x^(2)-3x+5 ?

    Text Solution

    |

  8. Assertion (A) : The tangent to the curve y=x^(3)-x^(2)-x+2 at (1,1) is...

    Text Solution

    |

  9. The function f(x) =x^(2)-2x increase forall

    Text Solution

    |

  10. Let a and b be two distinct roots of a polynomial equation f(x) =0 The...

    Text Solution

    |

  11. The profit fucntion in rupees of a firm selling x items (x ge 0) per w...

    Text Solution

    |

  12. A stone thrown vertically upward satisfies the equation s= 64 t -16t^(...

    Text Solution

    |

  13. If f(x)=3x^(2)+6x-9 then

    Text Solution

    |

  14. If x cos theta + y sin theta =2 is perpendicular to the line x-y =3 th...

    Text Solution

    |

  15. The function y=tan^(-1) x-x

    Text Solution

    |

  16. The velocity v of a particle at any instant t moving in a straight lin...

    Text Solution

    |

  17. The velocity of telegraphic comunication is given by v=x^(2) log (1//x...

    Text Solution

    |

  18. What is the maximum point on the curve x=e^(x)y ?

    Text Solution

    |

  19. A ballon is pumped at the rate of 4cm^(3) per second what is the rate ...

    Text Solution

    |

  20. If the function f(x)=k x^3-9x^2+9x+3 is monotonically increasing in ...

    Text Solution

    |