 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 following exercises 10 to 20, find the equation for the ellipse that satisfies the given condition. Thirteen is, n's of the major axis plus minus 3, 0 and n's of the minor axis 0, plus minus 2. An ellipse is the set of all the points in the plane. The sum of those distances from two fixed points in a plane is constant. Therefore, first let us draw an ellipse whose major axis is along the x-axis. So this ellipse, a is the length of the semi-major axis, therefore 2a is equal to the major axis, b is the length of the semi-minor axis, therefore 2b is the length of the minor axis, ab is the major axis and the series is the minor axis and the major axis is along the x-axis. And c, that is the distance of focus from centre is given by root over a square minus b square and the standard equation of an ellipse. In this case, that is when the major axis is along the x-axis is given by x square upon a square plus y square upon b square is equal to 1. The vertices of this ellipse is given by plus minus a, 0 and the focus f1 and f2 that is focus is given by plus minus c, 0. So with the help of these few ideas we will find the equation of the ellipse. So this is our key idea. Now let us start with the solution. So here we are given n's of major axis plus minus 3, 0 and the n's of minor axis 0, plus minus 2. Now here since the n's of the major axis lie on the x-axis since the y coordinate is 0, let us write it down since the n's of major axis on the x-axis plus the equation will be of the form x square upon a square plus y square upon b square is equal to 1 where a is the length of the semi major axis. Vertices are same as the n points of the major axis we have thus we have vertices is equal to plus minus 3, 0 since vertices are same as the n points of the major axis. So this implies that a is equal to 3 and let this be equation number 1 and the n's of minor axis 0 plus minus 2 are on the y axis therefore their distance from the centre of the ellipse is equal to the semi major minor axis sorry this implies that b is equal to 2. Let us denote this by equation number 2 and this is the standard form of equation of an ellipse. So let's substitute the value of a and b in this equation. So the equation of an ellipse using 1 and 2 can be written as x square upon 3 square plus y square upon 2 square is equal to 1 or we have x square upon 9 plus y square upon 4 is equal to 1. Hence the answer is the equation of an ellipse whose n points of the major axis are plus minus 3 comma 0 and n's of the minor axis are 0 comma plus minus 2 is x square upon 9 plus y square upon 4 is equal to 1. So this completes the session hope you have understood it take care and have a good day.