 Hello and how are you all today? The question says in each of the exercise 7 to 15, find the equation of the hyperbola satisfying the given conditions. The vertices are given to us as 0, plus minus 3 and the foci is given to us as 0, plus minus 5. Now, here the general equation of the hyperbola is y square by a square minus x square by b square is equal to 1 since the vertices and the foci lies on the y axis. Vertices is given to us as 0, plus minus a and here we are given the vertices as 0, plus minus 3. Thus we have the value of a as 3. Also we know that foci is equal to 0, plus minus c and here we are given the value of foci as 0, plus minus 5. Thus the value of c is equal to 5. Now with the help of the value of a and c, we can find out the value of b. Now we know that b square is equal to c square minus a square. Let us substitute the values we have. b square is equal to c square will be 25 and a square will be 9. So we have the value of b square equals to 16. So on substituting or putting the value of a as 3 and b square as 16, in the general equation of hyperbola, we have y square by a square that is 9 minus x square by b square that is found out. y square to be 16 is equal to 1. So this is the required answer that is the equation of the hyperbola. So this completes this session. Hope you enjoyed and understood it well.