Given equation of lines are \( \Large 5x+3y-7=0 \) ...(i) and \( \Large 15x+9y+14=0\ or\ 5x+3y+\frac{14}{3}=0 \) ...(ii) Therefore, Lines (i) and (ii) are parallel and \( \Large C_{1} \) and \( \Large C_{2} \) and of opposite signs, therefore these lines are on opposite sides of the origin, so the distance between them is \( \Large |\frac{C_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}| + |\frac{C_{2}}{\sqrt{a_{1}^{2}|+b_{2}^{2}}}| = |\frac{7}{\sqrt{5^{2}+3^{2}}}| + |\frac{14}{3\sqrt{5^{2}+3^{2}}}|\) \( \Large = |-\frac{7}{\sqrt{34}}| + |\frac{14}{3\sqrt{34}}| = \frac{35}{3\sqrt{34}} \)
