Tangent/normal/area for this Circle

  • #1
I'm not whether this is the right place, but I saw geometry, n differentiation n thought, hmm, my question kinda involves both. If its in the wrong place, sorry...

Anyways...Got this curve given as

:biggrin: = theta for the sake of typing, hehe.

x = a cos :biggrin: y = b sin :biggrin:

I established it's a circle, because cos^2 :biggrin: +sin^2 :biggrin: =1

and subbing that in what sin :biggrin: and cos :biggrin: equal gives (x/a)^2 + (y/b)^2 = 1

Which is in the form for an equation for a circle? I'm not entirely sure on all this 2 be honest so if I'm goin wrong, feel free 2 point it out.

I wanna find the tangent, the normal n the area of the circle. I've tried numerous ways but can't get the right answer.
 

Answers and Replies

  • #2
arildno
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"I established it's a circle, because cos^2:grumpy: +sin^2:grumpy: =1"

How does this identity establish the given curve as a circle?
It is an ellipse!!
The tangent is found by differentiating x and y with respect to :grumpy:
 
  • #3
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You have made a mistake because the parametrised circle is given as:
c(theta)=(a*cos(theta),a*sin(theta). (u have to take a=b)
so to obtain its tangent we need to differentiate c w.r.t. theta, giving
t=(-a*sin(theta),a*cos(theta)).
to obtain its normal we again differentiate t, giving
n=(-a*cos(theta),-a*sin(theta))/mag(n);
hope that satisfies u..
 

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