 Hello and how are you all there? My name is Priyanka and I shall be helping you with the following questions. It says in each of the exercise 7 to 15, find the equation of the hyperbola, satisfying the given conditions. Now here we are given foci as 0 comma plus minus root 10, that is passing through 2 comma 3. That means x, y is 2 and 3 respectively. Now the foci lie on the y-axis. Thus we have hyperbola of the general equation, y square by a square minus x square by b square is equal to 1. Now we know that foci is equal to 0 comma plus minus c. But here we are given it as 0 comma plus minus root 10. Thus we have the value of c as root 10, right? Also we are given that it is passing through 0.2 comma 3. Thus we have x square by a square minus x, y square by a square minus x square by b square is equal to 1. Now it can be written as 3 the whole square by a square minus 2 the whole square by b square is equal to 1. Let this be the first equation. Also we know that since b is equal to under root c square minus a square, so on putting a square as c square minus b square in the first equation. Here we have 9 divided by in place of a square. Now we need to write c square minus b square minus 4 divided by b square is equal to 1. That is 9 b square minus 4 c square plus 4 b square the whole divided by c square c square minus. That is b square bracket c square minus b square is equal to 1. Now transposing the denominator of the left hand side to the numerator of right hand side we have 9 b square minus 4 c square plus 4 b square equals to c square minus b square getting multiplied by b square. Now transposing all the elements to the left hand side we have 13 b square minus 4 c square is equal to now we can substitute the value of c square as 10. We have 10 minus b square the whole multiplied by b square. Again we have 13 b square minus 4 into 10 is equal to 10 minus b square multiplied by b square. Now we have 14 b square minus 4t minus 10 b square plus b raised to the power 4 is equal to 0. So we have b raised to the power 4 plus 3 b square minus 4t equals to 0. Which can be simplified further as b square minus 5 into b square plus 8 is equal to 0. That is the value of b square can be equal to 5 or the value of b square can be equal to minus 8. Now since b square since it is a square it cannot be negative so we have the value of b square equals to 5. Now since we know that we found out above that a square is equal to c square minus b square. Now let us find out the value of a square that will be root 10 the whole square minus 5 that is b square. That further implies a square is equal to 10 minus 5 that is equal to 5. The value of b square as well as a square this the general equation of hyperbola is y square divided by 5 minus x square divided by 5 is equal to 1. So this ends my session hope you enjoyed and understood it well have a nice day ahead.