 Hello and how are you all today? Let us discuss this question. It says in each of the following exercises 1 to 6, find the coordinates of the foci and the vertices, the eccentricity and the length of the latest rectum of the hyperbola. Now here, the equation of hyperbola is given to us as 9y square minus 4x square is equal to 36. Now before proceeding on we should be well versed with the standard equation of the hyperbola and that is y square by a square minus x square by b square is equal to 1 when the foci lies on the y axis. We have the foci as 0 comma plus minus c vertices as 0 comma plus minus 4 sorry a eccentricity as e is equal to c by a and the length of latest rectum is found by multiplying 2 by b square and dividing their product by a. Now let us proceed on with our solution. We have given the equation of hyperbola 9y square by 4x square is equal to 36. Now we will be dividing the whole equation by 36 as we want 1 over here and so that it will be easier for us to compare the given equation with the standard equation of the hyperbola. We have the answer as y square by 4 minus x square by 9 is equal to 36 right. Now we will be comparing it with standard equation known to us that is y square by a square minus x square by b square is equal to 1. So on comparing these two equations we have a square as 4 that means a is equal to plus minus 2 and b square as 9 that means the value of b is plus minus 3. Also we know the relation that b square is equal to c square minus a square so with the help of this relation we can find out the value of c square. b square is found out to be 9 so 9 is equal to c square minus e square that is 4 that implies we have 13 is equal to c square that further implies that the value of c is plus minus root 13. Now with the help of the known formulae we can find out all the four values. This we have foci as 0 comma plus minus c that is root 13 vertices as 0 comma plus minus a that is 2. The centricity that we refer as e is c by a that is root 13 by 2 and the length of latest victim is equal to 2 into b square that is 9 divided by 2 which gives us the value after simplification as 9. So these are the required answers to this session. Hope you understood the whole concept well and enjoyed learning maths. Bye for now.