 Hello and welcome to the session, the equation says in each of the following exercises 10 to 20 find the equation for the ellipse that satisfies the given condition center at the point 0, 0 major axis on the y axis and passes through the points 3, 2 and 1, 6. So, let us start with the solution, so here we are given that ellipse passes through the point 1, 6 and the major axis is on the y axis right, so that implies the standard equation of the ellipses x square upon b square plus y square upon a square is equal to 1 where a is the length of semi major axis and b is the length of semi minor axis, this equation of an ellipse passes through the point 1, 6 and 3, 2 therefore for the point 3, 2 equation of ellipse becomes 3 square upon b square plus y is 2 square upon a square is equal to 1, so we have 9 upon b square plus 4 upon a square is equal to 1, let us see equation number 1, also the ellipse passes through the point 1, 6, so for the point 1, 6 equation of ellipses given by 1 square upon b square plus 6 square upon a square is equal to 1 or we have 1 upon b square plus that is 6 upon a square is equal to 1, let us see equation number 2, now multiplying equation 2 by 9 we get 9 upon b square plus 324 upon a square is equal to 9, let us see equation number 3 and now subtracting equation number 1 from equation 3, we get 324 upon a square minus 4 upon a square since these two cancel out 9 upon b square minus 9 upon b square is 0, so we have 4 upon a square is equal to 9 minus 1 or we have 320 upon 8 is equal to a square and this implies that a square is equal to 40, now substituting a square is equal to 40 and equation number 2 we get 1 upon b square plus that is 6 upon 40 is equal to 1 or we have 1 upon b square is equal to 1 minus 36 upon 40 and this gives 4 upon 40 and 4 into 10s are 40, so we have b square is equal to 10, thus we have a square is equal to 40 and b square is equal to 10, now this is the standard equation of an ellipse whose major axis is along the y axis, so by substituting the value of b square and a square in this equation we shall be getting the equation of an ellipse, therefore equation of an ellipse is given by x square upon 10 plus y square upon a square that is 40 is equal to 1, hence our answer is equation of an ellipse whose center is at the point 0, 0 major axis on the y axis and passes through the point 3, 2 and 1 is given by x square upon 10 plus y square upon 40 is equal to 1, so this completes the session, hope you have understood it, take care and have a nice day.