Home
Class 12
MATHS
Find the curve passing through (2, 1) an...

Find the curve passing through (2, 1) and which has a constant subtangent equal to 2.

Text Solution

Verified by Experts

We are given that
sub-tangent `=y/((dy)/(dx))=k` (constant)
or `k(dy)/(y)=dx`
Integrating we get, `klogy=x+c`
Given, that curve passes through (2,1) `rArr c=-2`
Hence, the equation of such curve is `klogy=x-2`
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

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__

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of a and bdot

Find the equation to the curve passing through (2,2) and having its slope (-(x+y)/x) at the point (x,y)

Let C be a curve defined by y=e^(a+b x^2)dot The curve C passes through the point P(1,1) and the slope of the tangent at P is (-2)dot Then the value of 2a-3b is_____.

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x .

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

Find the equation of the curve which passes through the point (4, 3) and the gradient of the tengent to the curve at any point on it is equal to the reciprocal of the ordinate of the point.

Find the equation of a curve passing through the point (-2,3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2)) .

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through (0,1) and having gradient (-(y+y^3))/(1+x+x y^2) at (x , y) .

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. The slope of a curve, passing through (3,4) at any point is the recipr...

    Text Solution

    |

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

    Text Solution

    |

  3. Find the curve passing through (2, 1) and which has a constant subtang...

    Text Solution

    |

  4. lf length of tangent at any point on th curve y=f(x) intercepted betwe...

    Text Solution

    |

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

    Text Solution

    |

  6. Find the equation of the curve such that the portion of the x-axis c...

    Text Solution

    |

  7. Find the equation of the curve passing through the point, (5,4) if the...

    Text Solution

    |

  8. Find the equation of the curve passing through the origin if the middl...

    Text Solution

    |

  9. Find the equation of family of curves which intersect the family of cu...

    Text Solution

    |

  10. Find the orthogonal trajectory of y^2=4a x (a being the parameter).

    Text Solution

    |

  11. The population of a certain is known to increase at a rate proportiona...

    Text Solution

    |

  12. What constant interest rate is required if an initial deposit placed ...

    Text Solution

    |

  13. Suppose that a mothball loses volume by evaporation at a rate propo...

    Text Solution

    |

  14. A body at a temperature of 50^0F is placed outdoors where the temperat...

    Text Solution

    |

  15. Find the time required for a cylindrical tank of radius r and height H...

    Text Solution

    |

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

    Text Solution

    |

  17. A hemi-spherical tank of radius 2 m is initially full of water and h...

    Text Solution

    |

  18. Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

    Text Solution

    |

  19. Solve : {xcos(y/x)+ysin(y/x)}ydx={ysin(y/x)-xcos(y/x)}xdy

    Text Solution

    |

  20. Solve (dy)/(dx)=((x+y)^2)/((x+2)(y-2))

    Text Solution

    |