 Hello and welcome to the session. My name is Asha and I shall be helping you with the following question that says, in each of the exercise 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of latest rectum. Fifth one is x square upon 49 plus y square upon 36 is equal to 1. So let's start with the solution and here, the given equation of ellipse is x square upon 49 plus y square upon 36 is equal to 1 or it can further be written as x square upon 7 square plus y square upon 6 square is equal to 1. Now we know that an ellipse is the set of all the points in the plane, the sum of whose distance is from the two fixed point in the plane is constant. So here, please follow question number one of your book of this exercise before solving this problem where we have discussed the main points of the ellipse that will help us to give us a good idea of how we are going to proceed on with the solution. Now here as we can see the denominator of x square upon 49 is greater than the denominator of y square upon 36. Thus the major axis is along the x axis and the standard equation of ellipse is x square upon a square plus y square upon b square is equal to 1 if the major axis is along the x axis. Now on comparing the standard equation with the given equation of the ellipse we find here a is equal to 7 and b is equal to 6 thus c which is given by root over a square minus b square is equal to root over 49 minus 36 and this is equal to root over 13. Hence the two focus are given by plus minus c comma zero r root over 13 plus minus comma zero vertices given by plus minus a comma zero so we have plus minus 7 comma zero then we have the length of major axis is equal to 2 into a so we have 2 into 7 thus gives 14 and the length of minor axis is equal to 2 into b so we have 2 into 6 that is equal to 12 and its eccentricity is denoted by small e is given by c upon a that is root over 13 upon 7 and the length of the latest rectum which is given by 2 into b square upon a is equal to 2 into here b is equal to 6 so 36 upon a is 7 so thus gives 72 upon 7. Hence our answer is the focus of the given equation of the ellipse are plus minus root over 13 comma zero vertices are plus minus 7 comma zero the length of its major axis is equal to 14 the length of its minor axis is equal to 12 eccentricity e is root over 13 upon 7 and the length of the latest rectum is equal to 72 upon 7 so this completes the session hope you understood it take care and have a good day