 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 1, 2, 6, find the coordinates of the foci, the vertices, the eccentricity and the length of latest rectum. Here the given equation of the hyperbola is 49y square minus 16x square is equal to 784. Now here first of all we should be well versed with the standard equation of hyperbola when the foci lies on the y-axis and it is y square by a square minus x square by b square is equal to 1. Also we can find out the foci vertices eccentricity and the length of latest rectum by the known formulas. So let us proceed on with the solution. Here given the equation hyperbola is 49y square minus 16x square is equal to 784. Now on dividing the whole equation by 784 we have y square by 16 minus x square by 49 is equal to 1. Now on comparing it with standard equation that is y square by a square minus x square by b square is equal to 1. We have a square as 16 that means the value of a is plus minus 4 and b square as 49 that means the value of b is equal to plus minus 7. Also we know that b square is equal to c square minus a square it is quickly find out the value of c square it is 49 plus 16 is equal to c square that is further equal to 65 is equal to c square that gives us the value of c as root 65. Now answers are foci is equal to 0 comma plus minus c and that is root 65 obviously it will be having both the signs plus minus then the vertices is 0 comma plus minus a that is 4 then we have the eccentricity and that is c over a and lastly the length of latest rectum that is equal to 2b square and that is 49 divided by a that is 4. So we have the value as 49 by 2 right so these were the required answers to the question hope you understood it well and have a very nice day ahead.