Correct Answer: Option D

Explanation

2x\(^3\) - 4x + 2y\(^2\) - 6y - 2 = 0

Divide through by 2: x\(^2\) - 2x + y\(^2\) -3y -1 = 0

x\(^2\) -2x + y\(^2\) - 3y = 1

x\(^2\) -2x + 1 + y\(^2\) - 3y + \(\frac{9}{4}\)

= 1+ 1 + \(\frac{9}{4}\)

= (x- 1)\(^2\) (y - 3/2)\(^2\)

= \(\sqrt{\frac{17}{4}}\)

r = \(\frac{\sqrt{17}}{2}\)

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