(4) Consider the set C = {(x, y) = R² | y² = xº(1-x²)}. (a) Is C a curve? If yes, why yes? If no, why not? (b) Find a parametrisation of C and sketch C. Be sure to specify the domain of your parametrisation. Hint: a nice set of identities to consider are cos² () 2 sin (¹) cos (¹). sin t (c) Find the tangent line to C at (2,4). = 1+cost, sin² (1) 2 - 1-cos t and

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