One of the angle bisectors of the lines defined by the equation ax² + 2hxy + by² = 0 will intersect at the point of intersection of the lines represented by ax² + 2hxy + by² + 2gx + 2fy + c = 0 if the condition h(g² - f²) = fg(a - b) holds. The intersection point of the lines is identified as the center of the conic, given by specific coordinates. The angle bisector equation is hx² + (b - a)xy - hy² = 0. Substituting the intersection point into the bisector equation leads to a polynomial that simplifies to a product of factors. The condition ab - h² is always negative for conics consisting of two straight lines, confirming that the other factor must equal zero, thus proving the statement.