 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 one to nine 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. The third one is x square upon sixteen plus y square upon nine is equal to one So let's start with the solution And as we know an ellipse is the set of all the points in the plane the sum of whose distances From the two fixed point in a plane is constant Therefore with the help of Question number one where we have discussed some key ideas of the ellipse. We shall be solving this problem Now the given equation of the ellipse is x square upon sixteen plus y square upon nine is equal to one Or it can further be written as x square upon four square plus y square upon three square is equal to one Now here the denominator of x square upon sixteen is greater than the denominator of y square upon nine that is nine thus the major axis is alone the x axis and from question number one we know that a standard equation of the ellipse whose major Excesses along the x axis is given by x square upon a square Plus y square upon b square is equal to one now I'm comparing it with the general form of the equation of ellipse we find here that a is equal to four and b is equal to three Now let us find c c is equal to root over a square minus b square so we have root over 16 minus 9 and this is equal to root over 7 now the four guys that is the two focus f1 and f2 given by Plus minus c comma 0 so c is root over 7 so we have root over 7 plus minus comma 0 and the vertices are given by Plus minus a comma 0 so we have Plus minus 4 comma 0 since a is equal to 4 and we have to find the length of major axis This is equal to 2 times of it. So we have 2 into 4 is equal to 8 now let's find the length of Minor axis This is equal to 2 into b. So we have 2 times of 3 that is equal to 6 Now let us find the eccentricity is denoted by small e is equal to C upon a so we have root over 7 upon 4 and Lastly, let us find the length of Latest rectum and this is given by 2 to b square upon a so we have 2 Into 9 upon 4 and this is equal to 9 upon 2 Before solving this problem, please refer to question number 1 of this exercise where we have explained all The focus vertices length of major axis length of minor axis eccentricity length of latest victim and detail hence the answer is Okay of the given equation root over 7 Plus minus comma 0 What this is a given by plus minus 4 comma 0 the length of major axis Is equal to 8 and the length of minor axis is equal to 6 It's eccentricity is equal to root over 7 1 4 and the length of the Latest rectum is equal to 9 upon 2 So this completes the session. Hope you have understood it take care and have a good day