Find the equation of the circle concentric with the circle $2 x^{2} + 2 y^{2} + 8 x + 10 y - 39 = 0$ and having its area equal to $16 π$ square units.

2 x^{2} + 2 y^{2} - 3 x + y - 10 = 0

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3 x^{2} + y^{2} - 17 x - 19 y + 50 = 0

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4 x^{2} + 4 y^{2} + 16 x + 20 y - 23 = 0

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x^{2} + y^{2} - x - y = 0

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Solution

The correct option is C $4 x^{2} + 4 y^{2} + 16 x + 20 y - 23 = 0$
The equation of the given circle is
$2 x^{2} + 2 y^{2} + 8 x + 10 y - 39 = 0$
$⟹ x^{2} + y^{2} + 4 x + 5 y - 39 / 2 = 0$
The coordinates of its centre are $(- 2, - 5 / 2)$ . The required circle is concentric with the above circle, therefore the coordinates of its centre are $(- 2, - 5 / 2)$ .
Let r be the radius of the required circle. Then, its area is $π r^{2}$ . But it is given that its area is $16 π$ sq. units.
Therefore,
$π r^{2} = 16 π$
$r = 4$
Hence, the equation of the required circle is
$(x + 2)^{2} + (y + 5 / 2)^{2} = 4^{2}$
$4 x^{2} + 4 y^{2} + 16 x + 20 y - 23 = 0$

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Find the equation of the circle concentric with the circle 2x2+2y2+8x+10y−39=0 and having its area equal to 16π square units.

Find the equation of the circle concentric with the circle $2 x^{2} + 2 y^{2} + 8 x + 10 y - 39 = 0$ and having its area equal to $16 π$ square units.