 Hello and welcome to the session. The question says, in each of the exercises 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 of the ellipse. 8 thus 16 x square plus y square is equal to 16. Now let's start with the solution and the given equation of the ellipses 16 x square plus y square is equal to 16 or it can further be written as dividing both the sides by 16 we have x square plus y square upon 16 is equal to 1 or we have x square upon 1 square plus y square upon 4 square is equal to 1. And ellipse is the set of all the points in the plane such that the sum of whose distances from two fixed points in a plane is constant. Here we have the equation of Felix x square upon 1 square is equal to y square upon 4 square is equal to 1. Now here we can see that the denominator of y square upon 16 is greater than the denominator of x square upon 1 thus the major axis is along the y axis and the standard form of equation of an ellipse is given by x square upon b square plus y square upon a square is equal to 1 where the major axis is along the y axis. And to find the focus vertices length of major axis minor axis eccentricity and the length of latest rectum please refer to question number 2 of this exercise where we have explained that how do we find all these foci vertices major axis minor axis eccentricity and latest rectum that will help us to solve this problem. Now when comparing this standard equation with the given equation we find here that b is equal to 1 and a is equal to 4 thus c which is given by a square minus b square is equal to root over 4 square minus 1 square which is equal to root over 15 and thus the foci which are given by 0 comma plus minus c is equal to 0 comma plus minus root over 15 and the vertices which is given by 0 comma plus minus a is equal to 0 comma plus minus 4 and the length of major axis is given by 2 into a that is 2 into 4 which is equal to 8 and the length of minor axis is equal to 2 into b so 2 into 1 that is equal to 2. Now let's find the eccentricity denoting it by small e it is given by c upon a so c is root over 15 and a is 4 so this is the eccentricity and lastly it is find the length of latest rectum which is given by 2 into b square upon a that is 2 into b is equal to 1 so we have 1 square upon a is 4 so I am cancelling we have 2 into 2 is 4 so we have 1 upon 2. Hence the answer is for the given equation of the ellipse the foci has coordinates 0 and plus minus root over 15 its vertices are given by 0 comma plus minus 4 the length of major axis is equal to 8 and the length of minor axis is equal to 2 its eccentricity e is given by root over 15 upon 4 and the length of latest rectum is equal to 1 upon 2 so this completes the session take care and bye for now.