Home
Class 12
MATHS
The angle made by the tangent of the cur...

The angle made by the tangent of the curve `x = a (t + sint cost)`, `y = a (1+sint)^(2)` with the x-axis at any point on it is

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

The slope of the tangent to the curve x= 3t^(2) +1 , y=t^(3)-1 at x=1 is-

If x_(1) and y_(1) be the intercepts on the x and y-axis respectively of tangent to the curve x= a cos^(3) theta, y = b sin ^(3) theta at any point theta , on the then priove that, (x_(1)^(2))/(a^(2))+(y_(1)^(2))/(b^(1))=1

The angle between the tangents to the curves y=x^(2)andx=y^(2) at (1,1) is -

If the tangent to the curve x y+a x+b y=0 at (1,1) is inclined at an angle tan^(-1)2 with x-axis, then find a and b ?

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is

The line y = x + 1 is a tangent to the curve y^(2) = 4x at the point

The angle between the tangents to the curves y=sin x and y = cos x at their point of intersection is

The slope of the tangent to the curve x= t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is

Find the slope of tangent of the curve 3x^3+2x+y=0 at the point (1,-1)

The equation of the tangent to the curve (1+ x^(2) )y = 2- x where it crosses the x -axis is-

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Show that the square roots of two successive natural numbers greater ...

    Text Solution

    |

  2. If m is the slope of a tangent to the curve e^y=1+x^2, then (a)|m|>1 ...

    Text Solution

    |

  3. The angle made by the tangent of the curve x = a (t + sint cost), y = ...

    Text Solution

    |

  4. If f(x)=x^alphalogx and f(0)=0, then the value of alpha for which Ro...

    Text Solution

    |

  5. The value of ′c′ in Lagrange's mean value theorem for f(x)=x(x−2)^2 in...

    Text Solution

    |

  6. The point (s) on the curve y^3+3x^2=12y where line tangent is vertical...

    Text Solution

    |

  7. The triangle formed by the tangent to the curve f(x)=x^2+bx-b at the ...

    Text Solution

    |

  8. If the normal to the curve y=f(x) at the point (3,4) makes an angle (3...

    Text Solution

    |

  9. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

    Text Solution

    |

  10. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  11. If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 ...

    Text Solution

    |

  12. The tangent to the curve y=e^x drawn at the point (c,e^c) intersects t...

    Text Solution

    |

  13. Let S denote the set of all polynomials P(x) of degree lt=2 such tha...

    Text Solution

    |

  14. For the function f(x)=x^4(12(log)e x-7), show that the point (1,7) is...

    Text Solution

    |

  15. Let f(x)=log(2x-x^2)+sin((pix)/2)dot Then which of the following is/ar...

    Text Solution

    |

  16. Find the coordinates of the point on the curve y=x/(1+x^2)where the te...

    Text Solution

    |

  17. Show that 1+x ln(x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

    Text Solution

    |

  18. A swimmer S is in the sea at a distance d km from the closest point A ...

    Text Solution

    |

  19. Find the shortest distance of the point (0, c) from the parabola y=...

    Text Solution

    |

  20. If ax^2+b/xgecfor all positive x where agt0andbgtc show that 27ab^2ge4...

    Text Solution

    |