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Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)

Transform the given parametric equations into rectangular form. Then identify the-example-1
User JREAM
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1 Answer

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Answer:

Solution : Option D

Explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = 5cos(t) ⇒ x / 5 = cos(t)

y = 2sin(t) ⇒ y / 2 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / 5 )² = cos²(t)

+ ( y / 2 )² = sin²(t)

_____________

x² / 25 + y² / 4 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

User Brian Burns
by
6.2k points
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