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Tangent/normal/area for this Circle

  1. Jun 3, 2004 #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.
     
  2. jcsd
  3. Jun 3, 2004 #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:
     
  4. Jun 3, 2004 #3
    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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