Explanation:
C Given,
Equation circle is \(\mathrm{x}^2+\mathrm{y}^2+2 \mathrm{x}+4 \mathrm{y}-3=0\)
rewritten as, \((x+1)^2+(y+2)^2=(2 \sqrt{2})^2\)
Let, required point be \(\mathrm{Q}(\alpha, \beta)\)
Then, mid-point of \(\mathrm{P}(1,0)\) and \(\mathrm{Q}(\alpha, \beta)\) is the center of the circle \((-1,-2)\)
Then, \(\frac{\alpha+1}{2}=-1\)
\(\alpha+1=-2\)
\(\alpha=-3\)
and, \(\quad \frac{\beta+0}{2}=-2\)
\(\beta=-4\)So, required point is \((-3,-4)\)