Home
Class 12
MATHS
Let C be a curve such that the normal at...

Let C be a curve such that the normal at any point P on it meets x-axis and y-axis at A and B respectively. If BP : PA = 1 : 2 (internally) and the curve passes through the point (0, 4), then which of the following alternative(s) is/are correct?

A

The curve passes through`(sqrt10, -6)`

B

The equation of tangent at `(4,4sqrt3) is 2x +sqrt3y =20`

C

The differential equation for the curve is yy' + 2x = 0

D

The curve represent a hyperbola

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 3|52 Videos

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 4|29 Videos

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 1|30 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|15 Videos

  • ELLIPSE

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|20 Videos

Similar Questions

Explore conceptually related problems

A tangent and a normal to a curve at the point (x,y) make equal intercepts on the x -axis and they-axis respectively.Find the curve which passes through the point (1,1)

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 AB. The curve passen through the point (1,1). Determine the equation of the curve.

Tangent is drawn at any point P of a curve which passes through (1,1) cutting x -axis and y -axis at A and B respectively.If AP:BP=3:1, then

The number of normals to the curve 3y ^(3) =4x which passes through the point (0,1) is

Find the equation of the normal to the curve x^(2)=4y which passes through the point (1,2).

A tangent and a normal to a curve at any point P meet the x and y axes at A,B and C,D respectively.Find the equation of the curve passing through (1,0) if the centre of circle through O.C,P and B lies on the line y=x (where O is the origin).

A tangent to a curve at P(x, y) intersects x-axis and y -axis at A and B respectively.Let the point of contact divides AB in the ratio y^(2):x^(2)

MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. Find the particular solution of (cos x – x sin x +y^2)dx + 2xy dy = 0 ...

    Text Solution

    |

  2. Orthogonal trajectories of family of the curve x^(2/3)+y^2/3=a^((2/3))...

    Text Solution

    |

  3. The curve in the first quadrant for which the normal at any point (...

    Text Solution

    |

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

    Text Solution

    |

  5. Water is drained from a vertical cylindrical tank by opening a valv...

    Text Solution

    |

  6. If y=x/(In|cx|) (where c is an arbitrary constant) is the general solu...

    Text Solution

    |

  7. Number of straight lines which satisfy the differential equation (dy)/...

    Text Solution

    |

  8. If f''(x)+f'(x)+f^(2)(x)=x^(2) be the differentiable equation of a cur...

    Text Solution

    |

  9. If y= e^((k+1)x) is a solution of differential equation (d^2y)/(dx^2) ...

    Text Solution

    |

  10. The differential equation (d^2y)/dx^2+x dy/dx+siny+x^2=0, is which of...

    Text Solution

    |

  11. Let y = (A + Bx) e^(3x) is a solution of the differential equation(d^2...

    Text Solution

    |

  12. y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...

    Text Solution

    |

  13. Which one of the following is homogeneous function ?

    Text Solution

    |

  14. The graph of the function y = f(x) passing through the point (0, 1) an...

    Text Solution

    |

  15. (x^2y^3+xy)dy=dx

    Text Solution

    |

  16. The equation of the curve passing through (3,4) and satisfying the dif...

    Text Solution

    |

  17. The orthogonal trajectories of the system of curves y^2 =cx^3 are

    Text Solution

    |

  18. The solution the differential equation (dy/dx)^2 - (dy/dx)(e^x+e^(-x))...

    Text Solution

    |

  19. The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (...

    Text Solution

    |

  20. Let C be a curve such that the normal at any point P on it meets x-axi...

    Text Solution

    |