I think All Those answers specially first two (by some and jordão) answer the question clearly with conventional prototype base JS concept.
Now as you want the animal class constructor to behave according to the passed parameter to the construction, I think this is very much similar to basic behavior of Creational Patterns
for example Factory Pattern.
Here i made a little approach to make it work that way.
var Animal = function(type) {
this.type=type;
if(type=='dog')
{
return new Dog();
}
else if(type=="cat")
{
return new Cat();
}
};
Animal.prototype.whoAreYou=function()
{
console.log("I am a "+this.type);
}
Animal.prototype.say = function(){
console.log("Not implemented");
};
var Cat =function () {
Animal.call(this);
this.type="cat";
};
Cat.prototype=Object.create(Animal.prototype);
Cat.prototype.constructor = Cat;
Cat.prototype.say=function()
{
console.log("meow");
}
var Dog =function () {
Animal.call(this);
this.type="dog";
};
Dog.prototype=Object.create(Animal.prototype);
Dog.prototype.constructor = Dog;
Dog.prototype.say=function()
{
console.log("bark");
}
var animal=new Animal();
var dog = new Animal('dog');
var cat=new Animal('cat');
animal.whoAreYou(); //I am a undefined
animal.say(); //Not implemented
dog.whoAreYou(); //I am a dog
dog.say(); //bark
cat.whoAreYou(); //I am a cat
cat.say(); //meow