Home
Class 12
MATHS
The slope of the tangent to the curve at...

The slope of the tangent to the curve at any point is reciprocal of twice the ordinate of that point. The curve passes through the point `(4, 3)`. Determine its equation.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

Similar Questions

Explore conceptually related problems

The slope of a curve at any point is the reciprocal of twice the ordinate at that point and it passes through the point(4,3). The equation of the curve is:

The slope of a curve, passing through (3,4) at any point is the reciprocal of twice the ordinate of that point. Show that it is parabola.

A curve is such that the slope of the tangent to it at any point P is the product of ordinate of P and abscissa increased by 2. If it passes through (-4, e), then its equation is

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is

A curve in the first quadrant is such that the slope of OP is twice the slope of the tangent drawn at P to the curve, where O is the origin and P is any general point on the curve. If the curve passes through (4, 2), then its equation is

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

A curve passing through the point (1,2) and satisfying the condition that slope of the normal at any point is equal to the ratio of ordinate and abscissa of that point , then the curve also passes through the point

The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (-1,1).

The slope of the tangent to a curve at any point (x ,y) on its given by y/x-cot(y/x) . cos(y/x) ,(x >0,y >0) and the curve passes though the point (1,pi/4) . Find the equation of the curve.

Let C be a curve passing through M(2,2) such that the slope of the tangent at anypoint to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is A ,then the value of (3A)/2 i s__

RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Solve the differential equation: (dy)/(dx)+2y=sin x

    Text Solution

    |

  2. Solve the differential equation:(dy)/(dx)+y/x=x^2

    Text Solution

    |

  3. Solve x(dy)/(dx) +2y = x^2logx

    Text Solution

    |

  4. Find the general solution of the differential equations: (1+x^2)dy+...

    Text Solution

    |

  5. Solve the differential equation: y\ dx+(x-y^2)dy=0

    Text Solution

    |

  6. The differential equations, find a particular solution satisfying t...

    Text Solution

    |

  7. Find a particular solution of the differential equation: (x+y)dy+(x-y)...

    Text Solution

    |

  8. Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h ...

    Text Solution

    |

  9. Find the equation of the curve passing through the point (1,1) whose...

    Text Solution

    |

  10. Find the equation of a curve passing through the point (-2,3) , give...

    Text Solution

    |

  11. Find the equation of a curve passing through the point (0, 0) and wh...

    Text Solution

    |

  12. At any point (x, y) of a curve, the slope of the tangent is twice th...

    Text Solution

    |

  13. Show that the family of curves for which the slope of the tangent a...

    Text Solution

    |

  14. Find the equation of a curve passing through the point (0, 1). If t...

    Text Solution

    |

  15. Find the equation of a curve passing through the origin given that ...

    Text Solution

    |

  16. Find the equation of a curve passing through the point (0, 2) given...

    Text Solution

    |

  17. The slope of the tangent to the curve at any point is reciprocal of tw...

    Text Solution

    |

  18. The decay rate of radium at any time t is proportional to its mass at ...

    Text Solution

    |

  19. Experiments show that radium disintegrates at a rate proportional to t...

    Text Solution

    |

  20. A wet porous substance in the open air loses its moisture at a rate ...

    Text Solution

    |