 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 exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of latest rectum of the ellipse. 6th one is, x square upon 100 plus y square upon 400 is equal to 1. So let's start with the solution and here the given equation of the ellipse is, x square upon 100 plus y square upon 400 is equal to 1 or it can further be written as x square upon 10 square plus y square upon 20 square is equal to 1. Now please refer to question number 2 of this exercise before solving this problem to get a proper idea of an ellipse and its foci, vertices, length of major axis, minor axis, eccentricity and the length of latest rectum. Now here as we can see the denominator of y square upon 400 is greater than the denominator of x square upon 100. Therefore the major axis is along the y axis. Now the standard equation of the ellipse whose major axis is along the y axis is given by x square upon b square plus y square upon a square is equal to 1. Now when comparing the given equation with the standard equation of the ellipse we find here that a is equal to 20 and b is equal to 10. Now let us find c which is given by root over a square minus b square. So we have root over 400 minus 100 that is root over 300 or it can be written as 10 root 3. Let's focus given by 0 comma plus minus c. So we have 0 comma plus minus 10 root 3. Its vertices given by 0 comma plus minus a. So we have 0 comma plus minus 20 and the length of major axis which is given by 2 times of a. So we have 2 into 20 since a is equal to 20 we have 40 and the length of minor axis is given by 2 into b. So we have 2 into 10 and this is equal to 20. Now let's find the eccentricity. It is denoted by small e and given by c upon a and here c is 10 root 3 and a is 20. So we have root 3 upon 2 as the eccentricity. Now let us find the length of latest rectum. It is given by 2 times of b square upon a that is 2 ps 10 so we have 10 square upon a is 20. So we have 2 into 100 upon 20 and this comes equal to 10. Hence our answer is for the given equation of the ellipse spoke I have given by 0 comma plus minus 10 root 3. Its vertices are given by 0 comma plus minus 20. The length of the major axis is equal to 40. The length of the minor axis is equal to 20. The eccentricity e is given by root over 3 upon 2 and the length of the latest rectum is equal to 10. So this completes the session. Hope you have understood it. Take care and have a good day.