Correct Answer: Option A

Explanation

4x\(^2\) + 4y\(^2\) − 5x + 3y − 2 = 0

Divide through by 4

x\(^2\) + y\(^2\) - \(\frac{5}{4}\)x + \(\frac{3}{4}\)y = \(\frac{2}{4}\)

Add the square of half the coefficient of x and y to both sides

x\(^2\)  - \(\frac{5}{4}\)x + (\(\frac{-5}{8}\))\(^2\) + y\(^2\) + \(\frac{3}{4}\)y + (\(\frac{3}{8}\))\(^2\) = \(\frac{2}{4}\) + (\(\frac{-5}{8}\))\(^2\) +  (\(\frac{3}{8}\))\(^2\)

(\(\frac{x - 5}{8}\))\(^2\) + (\(\frac{y - 3}{4}\))\(^2\) = \(\frac{1}{2}\) + \(\frac{25}{64}\) +  \(\frac{9}{64}\)

Compare the above with: ( x - a)\(^2\) + ( y - b)\(^2\) = r\(^2\)

a = \(\frac{5}{8}\) and b = \(\frac{- 3}{8}\)

The coordinates of the centre(a,b) =  \(\frac{5}{8}\), \(\frac{- 3}{8}\).

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