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.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the curve whose length of the tangent at any point on ot, intercepted between the coordinate axes is bisected by the point of contact.

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, find the equation of the curve.

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

Find the length of tangent to the curve y=4x^3-2x^5 at (-1,1)

If the gradient of the tangent at any point (x,y) of a curve which passes through the point (1, (pi)/(4)) is {(y)/(x)-sin^(2)((y)/(x))} , then the equation of the curve is-

A curve is passing through the point (4,3) and at any point the gradient of the tangent to the curve is reciprocal of the ordinate of the point. Obtain the equation of the curve.

The equation of the tangent to the curve y= be^(-(x)/(a)) at the point where it crosses the y-axis is-

Show that the length of the tangent to the curve x^(m)y^(n)=a^(m+n) at any point of it, intercepted between the coordinate axes is divided internally by the point of contact in the ratio m:n.

Prove that the portion of the tangent to the curve (x+sqrt(a^2-y^2))/a=(log)_e(a+sqrt(a^2-y^2))/y intercepted between the point of contact and the x-axis is constant.

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).

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. A curve y=f(x) passes through the origin. Through any point (x , y) on...

    Text Solution

    |

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

    Text Solution

    |

  3. If length of tangent at any point on the curve y=f(x) intercepted be...

    Text Solution

    |

  4. For the primitive integral equation y dx+y^2dy=xdy ; x in R ,y >0,y(1...

    Text Solution

    |

  5. The solution of the primitive integral equation (x^2+y^2)dy=x ydx is ...

    Text Solution

    |

  6. If y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2) eq...

    Text Solution

    |

  7. If y(t) is a solution of (1+t)dy/dt-t y=1 and y(0)=-1 then y(1) ...

    Text Solution

    |

  8. The slope of the tangent at (x , y) to a curve passing through (1,p...

    Text Solution

    |

  9. The differential equation (dy)/(dx)=(sqrt(1-y^2))/y determines a f...

    Text Solution

    |

  10. Spherical rain drop evaporates at a rate proportional to its surface...

    Text Solution

    |

  11. Water is drained from a vertical cylindrical tank by opening a value a...

    Text Solution

    |

  12. The population of a country increases at a rate proportional to the...

    Text Solution

    |

  13. An object falling from rest in air is subject not only to the gravit...

    Text Solution

    |

  14. The solution of differential equation x^2=1 +(x/y)^(-1)(dy)/(dx)+((x...

    Text Solution

    |

  15. The solution of the differential equation y^(prime)y^(primeprimeprime)...

    Text Solution

    |

  16. Number of values of m in N for which y=e^(m x) is a solution of th...

    Text Solution

    |

  17. A curve passing through (2,3) and satisfying the differential equation...

    Text Solution

    |

  18. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

    Text Solution

    |

  19. The solution of the differential equations: (x+x^(3)/(3!)+x^(5)/(5!)...

    Text Solution

    |

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

    Text Solution

    |