Answer:
x²/9 +y²/64 = 1
Explanation:
You want the figure defined by x = 3sin(θ) and y = 8cos(θ) to be described by an equation in rectangular form.
Pythagorean identity
The trig identity sin(x)² +cos(x)² = 1 is helpful here.
x = 3sin(θ) ⇒ x/3 = sin(θ)
y = 8cos(θ) ⇒ y/8 = cos(θ)
Combining these using the above identity, we have ...
(x/3)² +(y/8)² = 1 . . . . . . the equation of an ellipse
We can simplify the denominators to ...
x²/9 +y²/64 = 1
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Additional comment
The attached graph uses different colors and textures to show the two forms of expressing the graph result in the same figure.