 Hello and welcome to the session my name is Arsha 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 14th is ends of major axis 0 comma plus minus root 5 and ends of minor axis are plus minus 1 comma 0. Now first it is draw an ellipse and as we know it is the set of all the points in a plane the sum of whose distances from two fixed points in a plane is constant so let this represent an ellipse and its major axis is along the y axis and some of its parameters are also given f and f to other focus ab is the major axis and cd is the minor axis so the length of the semi major axis is a and the length of the semi minor axis is b and the length of major axis is 2 and the length of minor axis is 2p and c which is the distance of focus from centre is given by root over a square minus b square 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 its vertices are given by 0 comma plus minus a and foci is given by 0 comma plus minus c let's now start with the solution and here ends of major axis is 0 plus minus root over 5 and the ends of minor axis plus minus 1 comma 0 this we are given major axis along the y axis thus the equation will be of the form square upon b square plus y square upon a square is equal to 1 since here the x coordinate is 0 and here a is the length of the semi major axis vertices at the end points of the major axis 0 comma plus minus root over 5 and since vertices is 0 comma plus minus a for this equation this implies that a is equal to root over 5 let this be equation number 1 and also the ends of minor axis that is plus minus 1 comma 0 are on the x axis so their distance from the centre of the ellipse is equal to the semi minor axis and this implies that b is equal to 1 and let this be equation number 2 now this is the standard equation so substituting a is equal to root over 5 and b is equal to 1 in the standard form of equation which is x square upon b square plus y square upon a square is equal to 1 to get the equation of an ellipse so we have x square upon 1 square plus y square upon root over 5 square is equal to 1 or we have x square plus y square upon 5 is equal to 1 hence our answer is the equation of an ellipse whose ends of the major axis are 0 comma plus minus root 5 and ends of minor axis are plus minus 1 comma 0 is x square upon 1 plus y square upon 5 is equal to 1 so this completes the session hope you have understood it well take care and have a good day