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Differential Calculus

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20 Sep 2007 17:56:34 IST

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tangentds and normals

None

prove that all the normals to the curve x=acost + atsint and y = a sint - atcost are at a distance 'a' from origin(a R⁺)

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tanmay gharat

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Joined: 24 May 2007

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20 Sep 2007 18:23:27 IST

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slope of any normal at point 't'=-cot t
eqn of normal is y-asint +acost=-cot t(x-acos t - atsin t)
we get y+cot t-asin t+acos tcot t=0
distance from origin=a

biki ....

Blazing goIITian

Joined: 5 Jun 2007

Posts: 978

20 Sep 2007 21:52:37 IST

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i' tell you the procedure....

first find out dy/dx for the curve.....[ dy/dx = (dy/dt) / (dx/dt) ]

take the slope at (x1,y1) say....

Now write the equation for normal at (x1,y1)....
as y - y1 = {-1 / (dy/dx) } (x - x1)

Now use the formula for perpendicular distance on a line from a point (here (0,0) ) to get the reqd. dist = a

biki ....

Blazing goIITian

Joined: 5 Jun 2007

Posts: 978

20 Sep 2007 21:54:20 IST

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hey tango goat........... check out my organic problem on inductive effect which you have already answered........i have some problems

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