Home
Class 12
MATHS
If length of tangent at any point on the...

If length of tangent at any point on the curve `y=f(x)`. Intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(1-y^2)-log |(1+sqrt(1- Y^2))/( 1-sqrt(1-y^2))|=+- x+c`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE )|28 Videos
  • DIFFERENTIAL CALCULUS 2

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

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

Similar Questions

Explore conceptually related problems

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

If the length of the portion of the normal intercepted between a curve and the x-axis varies as the square of the ordinate, find the equation of the curve.

The length of normal at any point to the curve, y=c cosh(x/c) is

A curve y=f(x) passes through the point P(1,1) . The normal to the curve at P is a(y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point. Determine the equation of the curve

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

The portion of tangent to curve x=√a^2-y^2 +- a/2 log a-√a^2-y^2 intercepted between curve and x axis is of length

Find the point on the curve y=x^2-2x+3 , where the tangent is parallel to x-axis.

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (" "4," "3) . Find the equation of the curve given that it passes through (2," "1) .

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-JEE ADVANCE (ARCHIVE )
  1. Integrating factor of sec^2y dy/dx+x tany=x^3

    Text Solution

    |

  2. Let u(x) and v(x) be two continous functions satisfying the different...

    Text Solution

    |

  3. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  4. A curve passes through the point (1,pi/6) . Let the slope of the curve...

    Text Solution

    |

  5. Tangent is drawn at any point P of a curve which passes through (1, 1...

    Text Solution

    |

  6. A spherical rain drop evaporates at a rate proportional to its surf...

    Text Solution

    |

  7. If length of tangent at any point on the curve y=f(x). Intercepted bet...

    Text Solution

    |

  8. A right circular cone with radius R and height H contains a liquid whi...

    Text Solution

    |

  9. A country has a food deficit of 10%. Its population grows continuously...

    Text Solution

    |

  10. A curve passing through the point (1,1) has the porperty that the perp...

    Text Solution

    |

  11. A and B are two separate reservoirs of water. Capacity of reservoir...

    Text Solution

    |

  12. Determine the equation of the curve passing through the origin, in ...

    Text Solution

    |

  13. If y=y(x) satisfies the differential equation 8sqrt(x)(sqrt(9+sqrt(x...

    Text Solution

    |

  14. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  15. Let y(x) be a solution of the differential equation (1+e^x)y^(prime)+y...

    Text Solution

    |

  16. Consider the family of all circles whose centers lie on the straight l...

    Text Solution

    |

  17. "Let "f:(0.oo)rarrR" be a differentiable function such that "f'(x)=2-...

    Text Solution

    |

  18. Let f:R to R be a differentiable function with f(0)=0. If y=f(x) satis...

    Text Solution

    |

  19. A solution curve of the differential equation (x^(2)+xy+4x+2y+4)(dy)/(...

    Text Solution

    |

  20. let T denote a curve y=f(x) which is in the first quadrant and let the...

    Text Solution

    |