Answer:
Option C
Explanation:
y2+4x2-12x+6y+14=0
4x2-12x+y2+6y+14=0
$4(x^{2}-3x+\frac{9}{4})+y^{2}+6y+9=-14+9+9$
$4(x-\frac{3}{2})^{2}+(y+3)^{2}=4$
$\frac{(x-3/2)^{2}}{1}+\frac{(y+3)^{2}}{4}=1$
Here, a2=1, b2=4
$\therefore$ $e=\sqrt{1-\frac{a^{2}}{b^{2}}}$
$e=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}$
