my old mac is not working. My old photos are there in my mac, most probably they are in i-photo. Is there any way to access those photos without the mac?

See if the problem Mac can startup in Target Disk Mode. If it can you can connect it to another Mac as the referenced document describes and access the hard drive to copy the library and any other needed files to the second Mac.

If you used iCloud photos your images will be at iCloud.com/photos and can be synched to any iPad or iPhone. If you have a Mac with a removable hard drive, you may be able to connect the drive to another Mac (depending on what you mean by your old Mac not working).

Or if you have a backup of the old mac, you should be able to recover the pictures from the backup.