Home
Class 12
MATHS
Prove that all points of the curve y^2=4...

Prove that all points of the curve `y^2=4a[x+asinx/a]` at which the langent is parallel to the axis of x, lie on a parabola.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Prove that all points on the curve y^(2)=4a[x+a sin(x/a)] at which the tangent is parallel to the x-axis lie on a parabola.

Prove that all the point on the curve y=sqrt(x+sinx) at which the tangent is parallel to x-axis lie on parabola.

Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the tangents are parallel to the x-axis.

At which point of the curve y=1+x-x^(2) the tangent is parallel to x-axis ?

For the curve x^(2)+4xy+8y^(2)=64 the tangents are parallel to the x-axis only at the points

For the curve x^(2)+4xy+8y^(2)=64 , the tangents are parallel to the x-axis only at the points-

The number of point in the rectangle {(x , y)}-12lt=xlt=12a n d-3lt=ylt=3} which lie on the curve y=x+sinx and at which in the tangent to the curve is parallel to the x-axis is (a) 0 (b) 2 (c) 4 (d) 8

Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

Find the point on the curve y^2=a x the tangent at which makes an angle of 45^0 with the x-axis.

Find points on the curve (x^(2))/(4) +(y^(2))/(25) =1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Find the possible values of p such that the equation p x^2=(log)e x ha...

    Text Solution

    |

  2. Find the angle between the curves 2y^2=x^3 and y^2=32 x.

    Text Solution

    |

  3. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

    Text Solution

    |

  4. Find the values of a if equation 1-cosx=(sqrt(3))/2|x|+ a ,x in (0,pi...

    Text Solution

    |

  5. Find the angle at which the curve y=K e^(K x) intersects the y-axis.

    Text Solution

    |

  6. Find the angle of intersection of the curves x y=a^2a n dx^2-y^2=2a^2

    Text Solution

    |

  7. Find the angle between the curves x^2-(y^2)/3=a^2a n dC2: x y^3=c

    Text Solution

    |

  8. Let f(x)=2x^3-9x^2+12 x+6. Discuss the global maxima and minima of f(x...

    Text Solution

    |

  9. If the curves a y+x^2=7 and x^3=y cut orthogonally at (1,1) , then fin...

    Text Solution

    |

  10. Discuss the extremum of f(x)=2x+3x^(2/3)

    Text Solution

    |

  11. Find the point on the curve 3x^2-4y^2=72 which is nearest to the line ...

    Text Solution

    |

  12. f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the con...

    Text Solution

    |

  13. Find the shortest distance between the line y=x-2 and the parabola y=x...

    Text Solution

    |

  14. f(x)={cos((pix)/2),x >0, x+a ,xlt=0 Find the values of ...

    Text Solution

    |

  15. If 1^0=alpha radians, then find the approximate value of cos60^0 1^(pr...

    Text Solution

    |

  16. If f(x)={{:(x^2,xlt=0) , (2sinx ,x >0):}' .Investigate the function at...

    Text Solution

    |

  17. If in a triangle ABC, the side c and the angle C remain constant while...

    Text Solution

    |

  18. If the function y=f(x) is represented as x=phi(t)=t^5-5t^3-20 t+7, ...

    Text Solution

    |

  19. Find the approximate value of(0. 0037)^(1/2) .

    Text Solution

    |

  20. Find the range fo the function f(x)=(x^(2)-x-6)/(x-3)

    Text Solution

    |