Find the separate equations of the straight lines represented by $2x^2 + 7xy + 3y^2 = 0$, and find the acute angle $\theta$ between them.

Prove that the equation $x^2 + 6xy + 9y^2 + 4x + 12y - 5 = 0$ represents a pair of parallel straight lines, and find the distance between them.

Find the separate equations of the straight lines represented by the homogeneous quadratic equation: $$2x^2 - 7xy + 3y^2 = 0$$ Also calculate the acute angle between these lines.

Find the value of $k$ so that the equation $$2x^2 + 5xy + 2y^2 + 7x + 5y + k = 0$$ represents a pair of straight lines. For this value of $k$, find their point of intersection.