 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 conditions. 16 to 1 is, length of minor axis is 16 and the focal is 0, plus minus 6. Now as we know an ellipse is a set of all the points in a plane, the sum of whose distance is from two fixed points in a plane is constant. Therefore first it is draw an ellipse, so this is an ellipse whose major axis is along the y axis, a b is the major axis and c d is the minor axis, small a is the length of semi major axis, therefore 2 a is the length of major axis and in this ellipse b is the length of semi minor axis, therefore 2 b is equal to the length of minor axis and the standard equation of an ellipse whose 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 here the major axis is along the y axis and the vertices are given by 0, plus minus a and the focal are given by 0, plus minus c. So with the help of these ideas we are going to find the equation of an ellipse, so this is our key idea. Now let's start with the solution, so here we have given the length of minor axis 16 and the foci 0, plus minus 6, now since the foci are on the y axis the equation will be of the form x square upon b square plus y square upon a square is equal to 1 and here a is the semi major axis and b is the semi minor axis and the focal are on the y axis since here the x coordinate is 0. Now by the key idea we know that length of minor axis and here we have given that length of minor axis is equal to 16 therefore we have 2b is equal to 16 or b is equal to 8 and the foci which is given to us as 0, plus minus 6 and the foci for this standard equation of an ellipse whose major axis is along the y axis is given by 0, plus minus c therefore comparing these two we find that here c is equal to 6. Now let us find the value of a since c is given by root over a square minus b square where c is the distance of focus from the centre therefore substituting the values of b and c we have 6 is equal to root over a square minus 8 square or 36 is equal to a square minus 64 or a square is equal to 64 plus third is x which is equal to 100 and b square is equal to 8 square since b is equal to 8 and this gives b square is equal to 64. Hence we have a square is equal to 100 and b square is equal to 64. So let us now substitute a square and b square in this standard equation to get the equation of an ellipse therefore equation of ellipse is given by x square upon 64 plus y square upon a square that is y square upon 100 so the value of a square is equal to 1. Hence the answer is equation of an ellipse whose length of minus x is 16 and the four guys given by 0 comma plus minus x is x square upon 64 plus y square upon 100 is equal to 1. So this completes the session. Bye and take care.