 Hello and welcome to the session. My name is Asha and I shall be helping you with the following question which says, in each of the following exercise 10 to 20, find the equation for the LF that satisfies the given condition. 18th is B is equal to 3, C is equal to 4 and centre at the origin and 4 chi on the x axis. So let's start with the solution and here we are given that B is equal to 3, C is equal to 4 and centre is at the origin 4 chi on the x axis. Now here we are given that focus is on the x axis. So this implies that the major axis is along the x axis and thus the standard equation of an LF given by x square upon a square plus y square upon b square is equal to 1 where a is the length of semi minor sorry major axis and B is the length of semi minor axis and for this standard equation the 4 chi is given by plus minus C comma 0 and C which is the distance of focus from the centre is given by a square minus b square. Now here we are given the values of b and c. So I am substituting the value of b and c in this equation let us find out a. So we have C as 4 is equal to root over a square minus b is 3 so we have 3 square. Squaring both sides we have 16 is equal to a square minus 9 or a square is equal to 16 plus 9 which is equal to 25. Therefore we have a square is equal to 25 and b square is b is given to us as 3 so we have 3 square is equal to 9. Now let us substitute a square is equal to 25 and b square is equal to 9 and the standard equation to get the equation of an LF which we are required to find so we have x square upon 25 plus y square upon 9 is equal to 1 as the equation of an LF for a given condition. The answer is the equation of an LF where b is equal to 3, c is equal to 4 and centre is at the original focus, y on the x axis is given by x square upon 25 plus y square upon 9 is equal to 1. So this completes the session hope you have understood it take care and have a good day.