Home
Class 12
MATHS
Show that the normal at any point theta ...

Show that the normal at any point `theta` to the curve `x = a cos theta + a theta sin theta, y = a sin theta - a theta cos theta` is at a constant distance from the origin.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|433 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 Videos

Similar Questions

Explore conceptually related problems

Find dy/dx when x = a (cos theta + theta sin theta) , y = a (sin theta - theta cos theta).

Eliminate theta between the equation : x =a cos theta + b sin theta, y =a sin theta- b cos theta .

Show that the equations of the normal at any point theta on the curve x = 3 cos theta - cos^3 theta, y = 3 sin theta - sin ^3 theta is 4(y cos^3 theta - x sin^3 theta) = 3 sin 4 theta

If x = a (cos theta + theta sin theta) and y = a (sin theta - theta cos theta) , find (d^2y)/(dx^2) at t = pi/4 .

Prove that : sin 2 theta= 2sin theta cos theta .

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Show that the curves 2x = y^2 and 2xy = k cut at right angles if k^2 =...

    Text Solution

    |

  2. Prove that the curves y^(2)=4axandxy=c^(2) cut at right angles if c^(4...

    Text Solution

    |

  3. Show that the normal at any point theta to the curve x = a cos theta +...

    Text Solution

    |

  4. Find the equations of the tangent and normal to the curve 16x^2 + 9y^2...

    Text Solution

    |

  5. Find a point on the curve y=x^(3), where the tangent to the curve is p...

    Text Solution

    |

  6. Find a point on the parabola y =(x-3)^2, where the tangent is parallel...

    Text Solution

    |

  7. Show that the area of the triangle formed by the tangent and the norma...

    Text Solution

    |

  8. Find the equations of the normal at a point on the curve x^2=4y, which...

    Text Solution

    |

  9. Find the equations of the tangents to the curve 3x^2 - y^2 = 8, which ...

    Text Solution

    |

  10. Determine the values of 'x' for which the function f(x) = x^2 + 2x - 3...

    Text Solution

    |

  11. Determine the intervals in which the function f(x) = (x-1)(x+1)^2 is i...

    Text Solution

    |

  12. Using differentials, find the approximate value of sqrt26

    Text Solution

    |

  13. Using differentials, find the approximate the value of root3(0.026) up...

    Text Solution

    |

  14. Find the approximate change in the volume V of a cube of side x metres...

    Text Solution

    |

  15. If the radius of a sphere is measured as 9 m with an error of 0.03 m, ...

    Text Solution

    |

  16. If y = x^4 + 10 and x changes from 2 to 1.99, find the approximate cha...

    Text Solution

    |

  17. Use differentials to calculating approximate value of loge(9.01)

    Text Solution

    |

  18. Use differentials to find the approximate value of tan46^@, if it is b...

    Text Solution

    |

  19. If in a DeltaABC, the side c and the angle C remain constant, while th...

    Text Solution

    |

  20. The time t of a complete oscillation of a simple pendulum of length l ...

    Text Solution

    |