Find the equation of the circle which is concentric with the circle $2 x^{2} + 2 y^{2} + 3 x - 4 y + 5 = 0$ and whose radius is $2 \sqrt{5}$ units.

4 x^{2} + 4 y^{2} + 6 x - 8 y - 55 = 0

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4 x^{2} + 4 y^{2} + 6 x - 8 y + 90 = 0

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4 x^{2} + 4 y^{2} + 6 x - 8 y + 57 = 0

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4 x^{2} + 4 y^{2} + 6 x - 8 y + 87 = 0

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Solution

The correct option is A $4 x^{2} + 4 y^{2} + 6 x - 8 y - 55 = 0$
Center of given circle = $(\frac{- 3}{2 \times 2}, \frac{4}{2 \times 2}) = (\frac{- 3}{4}, 1)$

Given $r = 2 \sqrt{5}$

Equation of circle with Center C(a,b) and radius r is

Equation of circle is $(x - a)^{2} + (y - b)^{2} = r^{2}$

Equation is $(x + \frac{3}{4})^{2} + (y - 1)^{2} = 4 \times 5$

$⟹ 4 x^{2} + 4 y^{2} + 6 x - 8 y - 55 = 0$

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