Explanation

(d)
Given equation can be rewritten as
$(x + 1)^{2} + (y + 2)^{2} = \left( 2\sqrt{2} \right)^{2}$
Let required point be $\mathcal{Q}(\alpha,\ \beta)$
Then. Mid point of $P(1,\ 0)$ and $\mathcal{Q}(\alpha,\ \beta)$ is the centre of the circle.
$ie,\ \ \frac{\alpha + 1}{2} = - 1$ and $\frac{\beta + 0}{2} = - 2$
$\Rightarrow \ \alpha = - 3\ \$and$\ \ \beta = - 4$
$\therefore$ required point is $( - 3,\ - 4)$