 Hello and how are you all there? The question says in each of the exercise 7 to 15, find the equation of the hyperbola, satisfying the given condition. Now here we are given foci as 0, plus minus 13 and the conjugate axis is a plane 24. Now let us proceed on with our solution. Now the foci lies on the y-axis thus we have the general equation of the hyperbola as y square by a square minus x square by b square is equal to 1. Now this is because the foci lies on the y-axis. Now we know that foci is equal to 0, plus minus c and here we are given foci as 0, plus minus 13. Thus we have the value of c equal to 13. Also we are given the length of conjugate axis as 24 and we know that the conjugate axis is equal to 2b right. So we have the value of b as 12. Also we know that b square is equal to c square minus a square. Now we know the value of b as 12 so it will be 12 the whole square is equal to c is 13, so 13 the whole square minus a square that further implies 144 is equal to 169 minus a square that is a square is equal to 25 right. Now we know the value of e as well as b. So the equation of hyperbola is y square by 5 the whole square minus x square by 12 the whole square that is b the whole square is equal to 1 or it is y square by 25 minus x square by 144 is equal to 1 that is on substituting the value of a as 5 and b as 12 in the standard equation. So to solve this equation we use the condition to find the equation of the hyperbola. So this is the required answer to this section. Hope you enjoyed and understood it well.