"place to live" and "place to live in"

[dcomest]

Hi!

I have a question.

Many people say both "place to live" and "place to live in" in such sentences as below:

a) I found a new place to live.
b) I found a new place to live in.

To the best of my knowledge, the sentence a) is grammatically incorrect. So I googled the two phrases and got the results as follows:

She is happy to have found such a nice place to live in.
Cambridge is an attractive place, and quite an easy place to live in.
The world will be a better place to live in.
Bali is a wonderful place to live in.
Few care about making the world a better place to live in.
.................................................. ....................................
It's a better place to live.
It's hard to find a place to live quickly.
I always dream of flying to USA because that's a wonderful place to live and to study.
Los Angeles is a pleasant place to live.
I found a new place to live, in West Ham.

Are both a) and b) grammartically acceptable/correct? If so, why?

Greatly looking forward to your insight.

Thanks in advance.

Jae From ROK

[Casiopea]

a) I found a new place to live.
b) I found a new place to live in.

Can you find the pattern?

live in a nice place
She is happy to have found such a nice place to live (in).
in Cambridge
Cambridge is an attractive place, and quite an easy place to live in.
live in the world
The world will be a better place to live in.
live in Bali
Bali is a wonderful place to live in.
live in the world
Few care about making the world a better place to live in.

*in a place to live / live in a better place
It's a better place to live (in).
*in a place to live
It's hard to find a place to live quickly.
live in the USA
The USA is a wonderful place to live (in) and to study.
live in LA
Los Angeles is a pleasant place to live (in).
live in a new place / *in a new place to live
I found a new place to live (in), in West Ham.