Price elasticity of demand is the degree of responsiveness of demand with a 1% change in price
demand curve will be parallel to the x axis when demand is perfectly elastic i.e without a change in price demand changes.

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It is the % change in quantity demanded in respsonse to 1% change in Price.
Price elasticity is usually negative.
If price elasticity of demand  (PED) is more than 1, then the price has a large effect on the quanity demanded.

It can be also written as  PED =  change in quantity / original quantity
                                                 change in price / original price
So x axis here is Quantity axis.
If the curve is parallel to x axis, it means The % change in price is always same what ever the quantity demanded is. This is perfectly elastic situation.

Suppose we are buying vegetables at Rs 10 a kg.  If we buy 2 kg its R20. if we buy 1/2 kg then Rs5.  If we buy 3 kg it costs Rs30. After buying 3 kg, if we buy 1 kg more it costs Rs10 more.  After buying 8 kg , if we buy 1 kg again, then it costsRs10 more .
SO you see, at any quanitity Q we have already purchased,  we want to buy 1kg more then it costs Rs10.  change in cost is Rs10 and
At any value of Q,  PED  =  change in quantity / original quantity = 1 / Q
                                        ---------------------------------------------------      --------
                                        change in price / price                          10 / P

But P = Rs 10 * Q    as P is the price of Q quantity of the vegetables.

So  PED  =  P/ 10 Q  = 10 Q/10 Q  = 1

PED is always same whatever the quantity already purchased.  So the curve is parallel to x axis and that is Q axis.