 Hello and welcome to the session. The question says, in each of the following exercises 10 to 20, find the equation for the ellipse that satisfies the given condition 15 to 1 is, length of major exercise 26 and foci is plus minus 5 comma 0. Now as we know, an ellipse has the set of all the points in the plane. The sum of force distances from two fixed point in a plane is constant. So first let us draw an ellipse. So the diagram represents the ellipse. Here its major axis is along the x-axis and AB is the major axis and CD is the minor axis. Here A is the length of semi-major axis, therefore 2A is equal to the length of major axis and B is the length of semi-minor axis. Therefore 2B is equal to the length of minor axis. 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 if the major axis is along the x-axis and also the vertices are given by plus minus 8 comma 0 and the foci that is the two focus F1 and F2 are given by plus minus 3 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. Let us now start with the solution. So we are given the length of major axis equal to 26 and also we are given the foci which are plus minus 5 comma 0 and since the foci are on the x-axis since the y-coordinate is 0 therefore the equation will be of the form square upon A square plus y square upon B square is equal to 1 where A is the semi-major axis. There we are given the length of the major axis is equal to 26 and for this equation of an ellipse the length of major axis is given by 2A is equal to 26 since the length of major axis is 2A this implies A is equal to 26 upon 2 that is 13. Let this be equation number 1. Now the foci for this equation of an ellipse are given by plus minus 3 comma 0 and on comparing it with the given foci that is this 5 comma 0 we get that C is equal to 5. Let this be equation number 2. Now we have A and C. Now let us find the value of B square which is given by A square minus C square since C which is the distance of focus from the center is given by A square minus B square therefore we have C square is equal to A square minus B square square in both the sides which further implies that B square is equal to A square minus C square. Now let us substitute the value of AMC so we have B square is equal to 13 square minus 5 square or 169 minus 25 which is equal to 144 so B square is equal to 144 and also A square is 13 mole square which is equal to 169. Now we have the value of B square and A square and since this is the standard equation of an ellipse whose major axis is along the x axis therefore now we shall be substituting the value of A square and B square to get the equation of an ellipse. Therefore equation of ellipse is given by x square upon A square and A square is 169 plus y square upon B square is 144 is equal to 1. Hence our answer is equation of an ellipse whose length of major axis is 26 and 4 chi is plus minus 5 comma 0 is given by x square upon 169 plus y square upon 144 is equal to 1. So this completes the solution hope you have understood it well take care and bye for now.