 Hello and welcome to the session. My name is Asha and I shall be helping you with the following equation that says, in each of the following exercises 10 to 20, find the equation for the ellipse that satisfies the given condition, 10th one is, what this is? Plus minus 5 comma 0 and the coordinates of 4 k r plus minus 4 comma 0. Now by the definition of ellipse we know that it is the set of all the points in a plane, the sum of those distances from the two fixed points in a plane is constant. If suppose this diagram represents the ellipse, here the major axis is along the x axis as we can see, some parameters of the ellipse are also shown in this figure F1 and F2 are the 4 k i, line a b is the major axis and Cd is the minor axis, points a and b are the two vertices and here a is the length of semi major axis, therefore 2a is equal to the length of major axis, similarly small b is the length of minor axis, sorry length of semi minor axis and therefore 2b is equal to the length of minor axis, which is the distance of focus on the centre is given by root over a square minus b square and the standard equation of the ellipse whose 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, here the major axis is along the x axis and the vertices of the ellipse whose major axis is along the x axis is given by plus minus a comma 0 and the 4 k i are given by plus minus c comma 0, so with the help of these few ideas we are going to find the equation of the ellipse, so this is our key idea, now let's start with the solution, now here we are given the vertices plus minus 5 comma 0 and the 4 k i plus minus 4 comma 0 and since the vertices are on the x axis equation of the ellipse will of the form x square upon a square plus y square upon b square is equal to 1 where a is the semi major axis and here since the vertices of this equation of the ellipse are given by plus minus a comma 0, therefore on comparing these two we will find here that a is equal to 5, similarly 4 k i are given by plus minus c comma 0 plus on comparing the given 4 k i which is plus minus 4 comma 0 we will find here that c is equal to 4, now since 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 4 is equal to root over 5 square minus b square or we have 16 is equal to 25 minus b square or b square is equal to 25 minus 16 which is equal to 9 or b is equal to plus minus 3, thus the equation of the ellipse is given by x square upon a square and a is 5, so we have 5 square plus y square upon b square, so first let us take b as 3, this is equal to 1, so this implies x square upon 25 plus y square upon 9 is equal to 1 is the equation of the ellipse for b is equal to 3, now let us find the equation of the ellipse for b is equal to minus 3, so this implies x square upon 5 square plus y square upon minus 3 square is equal to 1 or x square upon 25 plus y square upon 9 is equal to 1, hence our answer is equation of the ellipse with vertices plus minus 5, 0 and 4 chi plus minus 4, 0 is x square upon 25 plus y square upon 9 is equal to 1, so this completes the session, hope you have understood it well, take care and have a good day.