Find the equation of Circle concentric with $x^{2} + y^{2} + 3 x + 4 y + 1 = 0$ and passing through $(- 1, - 2)$ .

{(x + 2)}^{2} + {(y + 2)}^{2} = \frac{1}{4}

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

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

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

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Solution

The correct option is B ${(x + \frac{3}{2})}^{2} + {(y + 2)}^{2} = \frac{1}{4}$
Center of given circle = $(\frac{- 3}{2}, \frac{- 4}{2}) = (\frac{- 3}{2}, - 2)$

Let $(x + \frac{3}{2})^{2} + (y + 2)^{2} = r^{2}$ be a concentric circle

Given that this circle passes through (-1,-2)

$⟹ (\frac{1}{2})^{2} + 0^{2} = r^{2} = \frac{1}{4}$

Equation is $(x + \frac{3}{2})^{2} + (y + 2)^{2} = \frac{1}{4}$

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