r(t) = <acos t , bsin t>
Now, how about you go back, read the question again and the give it exactly.
In the first place an equation doesn't have a normal, a curve does.
If you mean, "find the equation for the normal to the curve given by r(t) = <acos t , bsin t> for any t", then say so.
Heres' a major hint the vector <a, b> is always normal to the vector <-b, a>.
In order to have a normal, you need to give us 1 set of coordinates.
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