Find the radius of the circle given by the equation
$2 x^{2} + 2 y^{2} + 3 x + 4 y + \frac{9}{8} = 0$ .

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Solution

The correct option is B $1$
In the given equation the coefficients of $x^{2}$ and $y^{2}$ are not unity. So, we re-write the equation to make the coefficients of $x^{2}$ and $y^{2}$ unity.

We have, $2 x^{2} + 2 y^{2} + 3 x + 4 y + \frac{9}{8} = 0$

$x^{2} + y^{2} + \frac{3}{2} x + 2 y + \frac{9}{16} = 0$

So, the coordinates of the centre are $(- 3 / 4, - 1)$ and thus, radius = $\sqrt{(\frac{3}{4})^{2} + (1)^{2} - \frac{9}{16}} = 1$

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