Let the area of the triangle formed by a straight line \( L: x + by + c = 0 \) with co-ordinate axes be \( 48 \) square units. If the perpendicular drawn from the origin to the line \( L \) makes an angle of \( 45^\circ \) with the positive \( x \)-axis, then the value of \( b^2 + c^2 \) is:
