 Hello and how are you all today my name is Priyanka and I shall be helping you with the following question. It says in each of the following exercises one to say find the coordinates of the Foucaille and the vertices, the eccentricity and the length of the latest rate. Now here the given equation of the hyperbola is 5y square minus 9x square equal to 36. So let us proceed on with our solution. As we are well aware of the standard equation of the hyperbola, when Foucaille lies on the y-axis and it is y square by a square minus x square by b square is equal to 1. So we shall be using the knowledge of this standard equation to proceed on with our solution. Here the given equation of hyperbola is 5y square minus 9x square is equal to 36. Now we shall be dividing the whole equation by 36 so that it will be easier for us to compare. So on doing so we have y square by 36 divided by 5. The 5 in the numerator has come to the denominator is denominator minus x square by 4 is equal to 1. Now on comparing it with the standard equation known to us that is y square by a square minus x square by b square is equal to 1. We have the value of a square as 36 by 5. That means the value of a is equal to plus minus 6 by root 5. Further we have the value of b square as 4. That means the value of b is plus minus 2. Now we know that b square is equal to c square minus a square. So with the help of the knowledge of b square and a square we can find out c square and hence the value of c. So it means b square is 4, c square is what we need to find out minus a square. That further implies 4 plus 36 by 5 is equal to c square that is 20 plus 36 the whole upon 5 is equal to c square which gives us the value of c square as 56 by 5 and hence the value of c is 2 root 14 divided by root 5. Thus we know that we can find out 4 chi as 0 comma plus minus c which is found out above as 2 root 14 by root 5. Further vertices is equal to 0 comma plus minus a that is 6 root 5 further centricity is c by a. So it will be 2 root 14 by root 5 the whole divided by 6 by root 5. Let us simplify it further. So we have the answer as root 14 in the numerator and 3 in the denominator. And lastly the length of latest written that is 2 into b square that is known to us as 4 divided by a that is 6 by root 5. Let us simplify it and on doing so we have the value of it as 4 root 5 the whole divided by 3. So these are the required answers to the question that was asked from us. This ends my session. Hope you enjoyed and understood the concept well. Have a very nice day ahead.