 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 exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions, 20th one is major axis on the x axis and passes through the points 4, 3 and 6, 2. Let's start with the solution and here we have given that the major axis is on the x axis, so this implies that the equation ellipse is of the form x square upon a square plus y square upon b square is equal to 1 where a is equal to the length of semi major axis and b is the length of semi minor axis. Now we are given that ellipse passes through the points therefore substituting the value of this first point where x is 4 and y is 3, in the equation of the ellipse we have 4 square upon a square plus 3 square upon b square is equal to 1 or we have 16 upon a square plus 9 upon b square is equal to 1, this is for the point 4, 3 and also the ellipse passes through the point 6, 2 therefore substituting x is equal to 6 and y is equal to 2, we have 6 square upon a square plus 2 square upon b square is equal to 1 or on simplifying it further we have 36 upon a square plus 4 upon b square is equal to 1 and this is for the point 6, 2. Let this be equation number 1 and this be equation number 2, now multiplying equation 1 by 4 and 2 by 9, 1 and 2 can be written as on multiplying this equation by 4 we have 16 4 to 64 upon a square plus 9 4 to 36 upon b square is equal to 4 and second equation implies on multiplying it with 9, 36 into 9 is 324 upon a square plus 9 4 to 36 upon b square is equal to 9, let us name this as equation number 3 and this as equation number 4. Now subtracting equation 3 from 4 we have it cancels out and we have 324 upon a square minus 64 upon a square is equal to 9 minus 4 which further implies that 200 and 60 upon a square is equal to 5 or a square is equal to 260 upon 5 which gives 52. Now substituting a square is equal to 52 in equation number 1 we have 16 upon 52 plus 9 upon b square is equal to 1 or we have 9 upon b square is equal to 1 minus 16 upon 52 which further implies 9 upon b square is equal to 52 minus 16 upon 52 this is equal to 36 upon 52 or b square is equal to 9 into 52 upon 36 9 4 to 36 and 4 into 13 is 52. So, we have b square is equal to 13 thus a square is equal to 52 and b square is equal to 13. Now substituting the values of a square and b square in this equation to get the standard equation of an ellipse where the major axis is on the x axis and passes through the point 4 3 and 6 2 therefore substituting a square is equal to 52 and b square is equal to 13 in the standard equation of an ellipse square upon a square that is 52 plus y square upon b square which is 13 is equal to 1 this can also be written as multiplying both the sides by 52 we have x square plus 4 y square is equal to 52. Hence our answer is equation of the ellipse is x square upon 52 plus y square upon 13 is equal to 1 or also it can be written as x square plus 4 y square is equal to 52. So, this completes the last question of this exercise. Hope you have understood this exercise well. Take care and have a good day.