Vibration in Drive Gear in Automatic Transmission

#1
I have a Corolla 2012 with 130,000 km (80,000 miles) on ODO and automatic transmission. I am the second owner and have only put 15,000 km on it. The problem is when I put the car in D gear (or even in R), the car starts to vibrate whereas, at P or N gear positions there is no vibration. Moreover, at D the RPM drops to 750 -800 though it remains at 1000 rpm in P or N. Is it a transmission problem or else? What should be done ?
 
#2
I have a Corolla 2012 with 130,000 km (80,000 miles) on ODO and automatic transmission. I am the second owner and have only put 15,000 km on it. The problem is when I put the car in D gear (or even in R), the car starts to vibrate whereas, at P or N gear positions there is no vibration. Moreover, at D the RPM drops to 750 -800 though it remains at 1000 rpm in P or N. Is it a transmission problem or else? What should be done ?
 
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