Calculus math help (includes vector/linear calc)?

Question

I have some questions plz tell answers and steps and stuff on how you find out.

4. Find the parametric equations for an ellispse of the form x^2/a^2 +y^2/b^2 = 1.
Tks for help

Plz show steps or explaination why!!!

Answer 1

x = asin∅
y = bcos∅
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Ideas: For any point (x,y) on the curve, x = asin∅ and y = bcos∅, where ∅ is the angle between the vector (x,y) and the x-axis.

Answer 2

Let x/a = cos z and y/b = sin z
Then x^2/a^2 +y^2/b^2 cos^2 z+sin^2 z = 1
So x= cos z and y = sinz are parametric equations of the ellipse x^2/a^2 +y^2/b^2 = 1.

Answer 3

Ok, let's try this method,

let x(t) = acos(t) and y(t) = bcos(t)

x^2(t)= a^2cos^2(t)
y^2(t) = b^2sin^2(t)

equation is now,

a^2cos^2(t) / a^2 + b^2sin^2(t) /b^2 = 1

cos^2(t) + sin^2(t) = 1

with the x, y substitutions shown above.

Good luck!