Home
Class 12
MATHS
A curve C passes through origin and has ...

A curve C passes through origin and has the property that at each point `(x, y)` on it the normal line at that point passes through `(1, 0)`. The equation of a common tangent to the curve C and the parabola `y^2 = 4x` is

A

x=0

B

y=o

C

y=x+1

D

x+y+1=0

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|13 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|9 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise For Session 5|8 Videos
  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

A curve has a property that the slope of the tangent at a point (x, y) is (y)/(x + 2y^(2)) and it passes through (1, 1). Find the equation of the curve.

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

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x^(2)-4x+y+8)/(x-2) , then this curve also passes through the point:

The slope of a curve at any point (x, y) on it is (4x-3) . If the curve passes through the point (1, 3), then its equation is

The slope of the tangent at a point P(x, y) on a curve is (- (y+3)/(x+2)) . If the curve passes through the origin, find the equation of the curve.

A curve passes through the point (0,1) and the gradient at (x,y) on it is y(xy-1) . The equation of the curve is

Find the equation of the normal at a point on the curve x^(2)=4y , which passes through the point (1,2). Also find the equation of the corresponding tangent.

The slope of tangent at a point P(x, y) on a curve is - x/y . If the curve passes through the point (3, -4) , find the equation of the curve.

Curve passing through (0,0) and slope of tangent to any point (x,y) is (x^2-4x+y+8)/(x-2) , then curve also passes through

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Single Option Correct Type Questions)
  1. If the differential equation of the family of curve given by y=Ax+Be^(...

    Text Solution

    |

  2. passes through a curve point (1,pi/4) and at some point Its gradation ...

    Text Solution

    |

  3. The x-intercept of the tangent to a curve is equal to the ordinate of ...

    Text Solution

    |

  4. A function y = f(x) satisfies the condition f'(x) sin x + f(x) cos x=...

    Text Solution

    |

  5. A curve is such that the area of the region bounded by the co-ordinate...

    Text Solution

    |

  6. The value of the constant 'm' and 'c' for which y = mx + c is a soluti...

    Text Solution

    |

  7. Find the real value of m for which the substitution y=u^m will transfo...

    Text Solution

    |

  8. The solution of the differential equation, x^(2)dy/dxcos""(1)/(x)-ysi...

    Text Solution

    |

  9. A wet porous subtance in the open air loses its moisture at a rate pro...

    Text Solution

    |

  10. A curve C passes through origin and has the property that at each poin...

    Text Solution

    |

  11. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

    Text Solution

    |

  12. The curve with the property that the projection of the ordinate on ...

    Text Solution

    |

  13. The differential equation corresponding to the family of curves y=e^x ...

    Text Solution

    |

  14. The equation to the orthogonal trajectories of the system of parabolas...

    Text Solution

    |

  15. A function satisfying int0^1f(tx)dt=nf(x), where x>0 is

    Text Solution

    |

  16. The substituion y=z^(alpha) transforms the differential equation (x^(2...

    Text Solution

    |

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

    Text Solution

    |

  18. Which one of the following curves represents the solution of the initi...

    Text Solution

    |