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Question

The parametric form of the ellipse 4(x+1)2+(y-1)2=4 is


A

x=cosθ1,y=2sinθ1

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B

x=2cosθ1,y=sinθ+1

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C

x=cosθ1,y=2sinθ+1

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D

x=cosθ+1,y=2sinθ+1

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E

x=cosθ+1,y=2sinθ1

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Solution

The correct option is C

x=cosθ1,y=2sinθ+1


Step 1: Convert the equation in the standard form

The equation of the given ellipse is,

4(x+1)2+(y-1)2=4

4(x+1)2+(y-1)24=44

(x+1)21+(y-1)24=1

(x+1)212+(y-1)222=1

Step 2: Convert into the parametric form

As we know the parametric equations of an ellipse of the form x2a2+y2b2=1 are,

x=acosθ and y=bsinθ

So, the parametric equations of the given ellipse are,

x+1=1cosθ

x=cosθ-1

And, y-1=2sinθ

y=2sinθ+1

Thus, the required parametric equations of the ellipse are x=cosθ-1 and y=2sinθ+1.

Hence, option (C) is the required option.


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