Explanation

(c)
Given equation of curve is $y^{2} + 2xy + x^{2} + 2x + 3y + 1 = 0$
Here $h^{2} = ab$, therefore the given curve is a parabola. The position of the point $(1, - 2)$ with respect to the parabola is obtained as ${( - 2)}^{2} + 2(1)( - 2) + {(1)}^{2} + 2(1) + 3( - 2) + 1 = - 2 < 0$
Since, point is inside the parabola therefore no tangent can be drawn to the parabola