Home
Class 12
MATHS
Find the normal to the curve x=a(1+cos ...

Find the normal to the curve `x=a(1+cos theta),y=a sintheta at theta.` Prove that it always passes through a fixed point and find that fixed point.

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 normal to the curve x= a(1 + cos theta ) , y= a sin theta at the point theta always passes throught the fixed point-

Find the slope of the normal to the curve x=a cos^(3) theta,y=a sin^(3) theta at theta=(pi)/(4) .

Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.

The normal to the curve x=a(costheta+thetasintheta),y=a(sintheta-thetacostheta) at any point theta is such that

The length of normal to the curve x=a(theta+sintheta),y=a(1-costheta) at theta=pi/2 is:

Let points A,B and C lie on lines y-x=0, 2x-y=0 and y-3x=0, respectively. Also, AB passes through fixed point P(1,0) and BC passes through fixed point Q(0,-1). Then prove that AC also passes through a fixed point and find that point.

If 3a +2b+c=0 for all positions of the moving line ax+by+c=0 , show that the line always passes through a fixed point . Find the coordinates of that fixed point.

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

If a+b+c=0 for all positions of the moving line ax+by+c=0 , show that the line always passes throught a fixed point . Find the coordinates of that fixed point.

Find the slope of the normal to the curve x=1 -a sin theta , y = b cos^(2) theta at theta= (pi)/(2) .

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let y=f(x) be drawn with f(0) =2 and for each real number a the line t...

    Text Solution

    |

  2. Let f:[0,oo)to[0,oo)a n dg:[0,oo)to[0,oo) be non-increasing and non-de...

    Text Solution

    |

  3. Find the normal to the curve x=a(1+cos theta),y=a sintheta at theta....

    Text Solution

    |

  4. If the curve C in the xy plane has the equation x^(2)+xy+y^(2)=1, then...

    Text Solution

    |

  5. Find the range of values of a if f(x)=2e^x-a e^(-x)+(2a+1)x-3 is monot...

    Text Solution

    |

  6. If the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, ...

    Text Solution

    |

  7. Is every invertible function monotonic?

    Text Solution

    |

  8. Let C be a curve defined by y=e^(a+b x^2)dot The curve C passes throug...

    Text Solution

    |

  9. If the line xcostheta+ysintheta=P is the normal to the curve (x+a)y=1...

    Text Solution

    |

  10. Prove that f(x)=x-sinx is an increasing function.

    Text Solution

    |

  11. Let f defined on [0, 1] be twice differentiable such that |f "(x)| ...

    Text Solution

    |

  12. If the tangent at any point (4m^2,8m^2) of x^3-y^2=0 is a normal to th...

    Text Solution

    |

  13. f(x) = cosx-2ax monotonically decreases when

    Text Solution

    |

  14. If a , b are two real numbers with a<b then a real number c can be fo...

    Text Solution

    |

  15. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  16. Separate the intervals of monotonocity of the function: f(x)=3x^4-8x^...

    Text Solution

    |

  17. Column I, Column II A circular plate is expanded by heat from ra...

    Text Solution

    |

  18. Find the total number of parallel tangents of f1(x)=x^2-x+1a n df2(x)=...

    Text Solution

    |

  19. Separate the intervals of monotonocity of the function: f(x)=-sin^3x+...

    Text Solution

    |

  20. The angle between the curves y^2 =4x+4 and y^2 =36(9−x) is?

    Text Solution

    |