Question

Eliminate θ from x = a cos³ θ; y = b sin³ θ

Answer 1

Please see the attachment

Answer 2

Solution :

Here I am using A instead of theta.

i ) x = acos³A

=> x/a = cos³A

=> ( x/a )^⅓ = cosA -----( 1 )

ii ) y = bsin³A

=> y/b = sin³A

=> ( y/b )^⅓ = sinA ------( 2 )

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We know the Trigonometric identity:

cos²A + sin²A = 1

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From ( 1 ) & ( 2 ) ,

=> ( x/a )^2/3 + ( y/b )^2/3 = 1

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