 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 exercises 7 to 15 Find the equation of the hyperbola satisfying the given conditions Here we are given that the vertices is equal to plus minus 7 comma 0 and the eccentricity is given to us as 4 by 3 now before proceeding on with the solution we should be well worse that the general equation of a hyperbola is x square by a square minus y square by b square is equal to 1 where the vertices are plus minus a comma 0 Also the eccentricity that is e is equal to c by a and the length of the latest rectum is to b square by a so with the knowledge of all these Conditions we shall be proceeding on with our solution now the hyperbola with vertices plus minus 7 comma 0 and eccentricity is given to us as 4 by 3 as we know That the vertices lie on the x axis thus we have the hyperbola's general equation as x square by a square minus y square by b square is equal to 1 now the vertices is Also equal to plus minus a comma 0 so that means here we have the value of a as 7 and eccentricity is given to us as 4 by 3 which is Equal to c by a Now we know the value of a as 7 so we can find out the value of c and it will be 28 by 3 Now we shall be proceeding on to find out the value of b that is C square minus a square we have b as C square is 28 by 3 the whole square minus a is 7 the whole square that is a square so we have the value of a as 784 by 9 minus 49 the all-in-square root that is After taking the else in 348 3 by 9 That is further equal to So b square is further equal to squaring both the side 343 by 9 now we know the value of a is equal to 7 b is equal to sorry b square is equal to 343 by 9 and C is equal to 28 by 3 now on substituting the values of a and b equation we get x square by a square Minus y square by b square that is 343 by 9 is equal to 1 or We can write it as x square by 49 minus 9 y square by 343 is equal to 1 and Thus this is the required equation of the hyperbola So this completes the session. Hope you enjoyed and understood the concept well. Have a very nice day ahead