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.

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
PRADEEP PUBLICATION|Exercise EXERCISE|502 Videos
APPLICATIONS OF INTEGRALS
PRADEEP PUBLICATION|Exercise EXERCISE|162 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.

PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE

The two equal sides of an isosceles triangle with fixed base b are dec...
Text Solution
|
Find the slope of the normal to curve xy = 6 at point (1,6)
Text Solution
|
Show that the normal at any point theta to the curve x = a cos theta +...
Text Solution
|
Find the intervals in which the function f given by f(x) = (4 sinx-2x-...
Text Solution
|
Find the intervals in which the function f given by f(x) = (4 sinx-2x-...
Text Solution
|
Find the intervals in which the function f given by f(x) = x^3 + (1/x^...
Text Solution
|
Find the intervals in which the function f given by f(x) = x^3 + (1/x^...
Text Solution
|
Find the maximum area of an isosceles triangle inscribed in the ellips...
Text Solution
|
A tank with rectangular base and rectangular sides, open at the top is...
Text Solution
|
The sum of the perimeter of a circle and square is k, where k is some ...
Text Solution
|
A window is in the form of a rectangle surmounted by a semi-circular o...
Text Solution
|
A point on the hypotenuse of a triangle is at distance a and b from th...
Text Solution
|
Find the points at which the function f given by f(x) = (x-2)^4(x+1)^3...
Text Solution
|
Find the points at which the function f given by f(x) = (x-2)^4(x+1)^3...
Text Solution
|
Find the points at which the function f given by f(x) = (x-2)^4(x+1)^3...
Text Solution
|
Find the absolute maximum and minimum values of the function f given b...
Text Solution
|
Show that the altitude of the right circular cone of maximum volume th...
Text Solution
|
Let f be a function defined on [a, b] such that f'(x)>0 for all x in ...
Text Solution
|
Show that the height of the cylinder of maximum volume that can be ins...
Text Solution
|
Show that height of the cylinder of greatest volume which can be inscr...
Text Solution
|