The long-run average cost curve is longer.

what is the relationship between long run average cost curve and short run average cost curve?

The long run average total cost curve is the lowest average total cost for producing each level of output. It depicts the per unit cost of producing a good or service in the long run when all inputs are variable.

the long run curve is at a minimum point

Long run average cost curve is known as envelope curve because it is formed by enveloping the short run average cost curves and it helps the entrepreneur in long term planning that is why it is also called planning curve.