The co-ordinates of centre of the circle $3 x^{2} + 3 y^{2} - 9 x + 15 y + 4 = 0$

\frac{9}{2}, \frac{- 15}{2}

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\frac{- 9}{2}, \frac{15}{2}

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\frac{3}{2}, \frac{- 5}{2}

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None of these

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Solution

The correct option is C $\frac{3}{2}, \frac{- 5}{2}$
Given equation is,
$3 x^{2} + 3 y^{2} - 9 x + 15 y + 4 = 0$
$\Rightarrow x^{2} + y^{2} - 3 x + 5 y + \frac{4}{3} = 0$
Comparing it with the standard equation, we get
Center: $(- g, - f) = (\frac{3}{2}, \frac{- 5}{2})$

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