The answer is ЭТО ТВОЯ КОШКА? In Russian possessive pronouns change depending on the gender of a noun (masc., fem., neutr.) and in plurals : МОЙ дом, МОЯ машина, МОЁ письмо, МОИ дети ТВОЙ дом, ТВОЯ машина, ТВОЁ письмо, ТВОИ дети НАШ дом, НАША машина, НАШЕ письмо, НАШИ дети ВАШ дом, ВАША машина, ВАШЕ письмо, ВАШИ дети However, ЕГО, ЕЁ, ИХ don't change: ЕГО дом, ЕГО машина, ЕГО письмо, ЕГО дети. This is all only about Nominative case (in other cases the endings will be different). We usually use Nominative: 1) when our noun (together with its possessive pronoun) is a subject in a sentence: МОЯ КОШКА ЛЮБИТ МОЛОКО (My cat likes milk) *You can put МОЙ КОТ if it is a he-cat. 2) After the word ЭТО (This is/These are): ЭТО МОЯ КОШКА (This is my cat) ЭТО ТВОЯ КОШКА? (Is this your cat?) 3) When we want to say that we have something - a construction У (меня, тебя, его её, нас, вас, их) ЕСТЬ....: У МЕНЯ ЕСТЬ КОШКА (I have a cat) So, because you asked how to say "Is that your cat" and you need to use ЭТО - you simply need to use an easy Nominative case here - luckily, not a Genitive at all :) That's why ЭТО ТВОЯ КОШКА? is perfectly fine :)

Dear Troy, some russians are confused about cases at all :) The nominative case - Это твоя кошка (case's question кто? или что?) And I have a secret how you can know the genitive case from the accusative one. And a tell you :) If you can add the word "нет" it is genetive case. If you can add the word "вижу" it is accusative case. The genitive - морда твоей кошки - (case's question кого? или чего?). "нет кошки" The accusative - глажу твою кошку - (case's question кого? или что?) "вижу кошку" Each case has its own bridging word :) Probably you have already known them.

Hello, Troy, The first question is right if you speak about female cat. If you speak about male cat (tomcat) the right question would be: Это твой кот?. If you don't know the sex of a pet or don't care about it you can use both questions.

Here you can read about Genitive Case http://learnrussian.rt.com/grammar-tables/nouns-singular-in-the-genitive-sase/ Это твоя кошка? is correct. It is Nominative Case. It answers the questions Кто? Что? - Это твоя кто? Кошка. Genitive Case is used with твоЮ - Я люблю твою кошкУ ( It answers the questions Кого? Чего?)

Usage of Genitive case is much more complicated, there are a lot more situations when we need to use it, but that's a different story. The tricky thing is that the whole collection of the pronouns described above will also change in Genitive case (together with nouns) - as well as in other Russian cases. So, for example, твой дом (Nominative) becomes твоего дома (Genitive); твоя машина becomes твоей машины, твоё письмо - твоего письма, твои дети - твоих детей. But it's a completely sepatate topic :)