 Hello and how are you all today? My name is Priyanka and let us discuss this 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 vertices is equal to plus minus 2 comma 0 and the foci is plus minus 3 comma 0. Now with the help of the given vertices and foci, we need to find out the equation of the hyperbola. So let us be first, be well versed with the standard equation of a hyperbola that is x square by a square minus y square by b square is equal to 1. Here the foci is given to us as plus minus c comma 0 and the vertices are plus minus a comma 0. This is the center. Now here the line passing through the foci is called the transverse axis and the line which is perpendicular to the transverse axis and passing through the center is called the conjugate axis. Now here we need to find out the standard equation of a hyperbola. So let us be first, well versed with one of the equations that says that b is equal to square root of c square minus a square. Now the knowledge of this relation is the key idea for this question. Let us proceed on with our solution. Here the hyperbola with vertices plus minus 2 comma 0 and foci plus minus 3 comma 0 is given to us. We know that the vertices foci lie on the x axis thus we have, we know that the foci and the vertices they both lie on the x axis that is the transverse axis. So we have the general equation of the hyperbola as x square by a square minus y square by b square is equal to 1. Here the vertices are plus minus a comma 0 foci is equal to plus minus c comma 0. Now here we are given vertices in the question as plus minus 2 comma 0 and foci as plus minus 3 comma 0. So thus we can say that a is equal to 2 and c is equal to 3. Now with the help of the values of a and c we can find out the value of b. So next we know that b is equal to under the root c square minus a square. Let us quickly substitute the values. So we have c square as 3 the whole square minus a square as 2 the whole square that implies b is equal to under the root 3 square is 9 minus 2 square is 4 that is under the root 5. So the equation of hyperbola is x square by a square that is 4 minus y square by b square it will be root 5 into root 5 that means 5 is equal to 1. So this is the required equation of the hyperbola. So to solve this question we use the given conditions to find the equation of the hyperbola. Hope you enjoyed the session ok bye and take care.