Replying to Ticks on my cat. Questions.

 Sorry to clog up NSG with this stuff andI know this thread will prolly be deleted soon but, i found maybe 4 large ticks on my cat and pulled them off. Then i found some large juicy bastards in the couch she was just on, And there are like a couple more little ones on her. Question: Do they lay eggs? and How fast do they multiply?

Not looking for hate, just asking because she is old and there were a shit ton on her. +K for answers.