 Hello and welcome to the session, the given question says, in each of the following exercises 10 to 20, find the equation for the ellipse that satisfies the given condition. Eleventh one is, vertices are given by 0, plus minus 13 and 4 chi is 0, plus minus 5. Now by the definition of ellipse, we know that it is the set of all the points in a plane, and the sum of those distances from two fixed points in a plane is constant. So, first we just draw an ellipse whose major axis is along the y axis. Suppose this is an ellipse whose major axis is along the y axis, so here a b denotes the major axis of the ellipse and c d denotes the minor axis of the ellipse and a and b are the vertices of the ellipse and these two denotes the 4 chi of the ellipse and the standard equation of ellipse, in the case when the 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 and a is the length of semi major axis therefore 2a is equal to the major axis and b is the length of semi minor axis therefore 2b is equal to the length of minor axis and the vertices of the ellipse whose major axis is along the y axis are given by 0 comma plus minus a and its 4 chi is given by 0 comma plus minus c. So, with the help of these ideas we shall find the equation of the ellipse, so this is our key idea. Let us now start with the solution. So, here we have given the vertices 0 comma plus minus 13 and the 4 chi as 0 comma plus minus 5. Now we can see that the vertices as well the 4 chi lie on the y axis since the coordinate of x is 0 in both the cases therefore the major axis of the given ellipse is along the y axis. Let us write it down since the vertices are on the y axis therefore the equation will be of the form x square upon b square plus y square upon a square is equal to 1 where a is the semi major axis and b is the semi minor axis and here since we are given that both theses are 0 comma plus minus 13 thus on comparing we find that a is equal to 13 and since the 4 chi is 0 comma plus minus 5 and the 4 chi of the standard equation of an ellipse whose major axis is along the y axis is 0 comma plus minus c. So, the simple as c is equal to 5. Now as we know c is equal to root over a square minus b square. So, let us substitute the value of a and c to get the value of b, c is 5 root over 13 square minus b square I was wearing both sides we have 25 is equal to 169 minus b square which implies that b square is equal to 169 minus 25 which is equal to 144 or b is equal to plus minus 12. Now the standard equation of the ellipses given by square upon b square plus y square upon a square is equal to 1. So, for b is equal to plus minus 12 and a is equal to 13 the standard equation is given by x square upon b square plus y square upon 12 plus minus 12 whole square plus y square upon 13 square is equal to 1 or we have x square upon 144 plus y square upon 169 is equal to 1. Hence equation of the ellipse for which the vertices are given by 0 plus minus 13 and the 4 chi is given by 0 comma minus 5 comma plus minus 5 is x square upon 144 plus y square upon 169 is equal to 1. So, this completes the session hope you understood it well take care and have a nice day.